Factors of 9000 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 45, 50, 60, 72, 75, 90, 100, 120, 125, 150, 180, 200, 225, 250, 300, 360, 375, 450, 500, 600, 750, 900, 1000, 1125, 1500, 1800, 2250, 3000, 4500, and 9000

How to find factors of a number

1. Steps to find factors of 9000 using Division Method

Example: Find factors of 9000

  • Divide 9000 by 1: 9000 ÷ 1 : Remainder = 0
  • Divide 9000 by 2: 9000 ÷ 2 : Remainder = 0
  • Divide 9000 by 3: 9000 ÷ 3 : Remainder = 0
  • Divide 9000 by 4: 9000 ÷ 4 : Remainder = 0
  • Divide 9000 by 5: 9000 ÷ 5 : Remainder = 0
  • Divide 9000 by 6: 9000 ÷ 6 : Remainder = 0
  • Divide 9000 by 8: 9000 ÷ 8 : Remainder = 0
  • Divide 9000 by 9: 9000 ÷ 9 : Remainder = 0
  • Divide 9000 by 10: 9000 ÷ 10 : Remainder = 0
  • Divide 9000 by 12: 9000 ÷ 12 : Remainder = 0
  • Divide 9000 by 15: 9000 ÷ 15 : Remainder = 0
  • Divide 9000 by 18: 9000 ÷ 18 : Remainder = 0
  • Divide 9000 by 20: 9000 ÷ 20 : Remainder = 0
  • Divide 9000 by 24: 9000 ÷ 24 : Remainder = 0
  • Divide 9000 by 25: 9000 ÷ 25 : Remainder = 0
  • Divide 9000 by 30: 9000 ÷ 30 : Remainder = 0
  • Divide 9000 by 36: 9000 ÷ 36 : Remainder = 0
  • Divide 9000 by 40: 9000 ÷ 40 : Remainder = 0
  • Divide 9000 by 45: 9000 ÷ 45 : Remainder = 0
  • Divide 9000 by 50: 9000 ÷ 50 : Remainder = 0
  • Divide 9000 by 60: 9000 ÷ 60 : Remainder = 0
  • Divide 9000 by 72: 9000 ÷ 72 : Remainder = 0
  • Divide 9000 by 75: 9000 ÷ 75 : Remainder = 0
  • Divide 9000 by 90: 9000 ÷ 90 : Remainder = 0
  • Divide 9000 by 100: 9000 ÷ 100 : Remainder = 0
  • Divide 9000 by 120: 9000 ÷ 120 : Remainder = 0
  • Divide 9000 by 125: 9000 ÷ 125 : Remainder = 0
  • Divide 9000 by 150: 9000 ÷ 150 : Remainder = 0
  • Divide 9000 by 180: 9000 ÷ 180 : Remainder = 0
  • Divide 9000 by 200: 9000 ÷ 200 : Remainder = 0
  • Divide 9000 by 225: 9000 ÷ 225 : Remainder = 0
  • Divide 9000 by 250: 9000 ÷ 250 : Remainder = 0
  • Divide 9000 by 300: 9000 ÷ 300 : Remainder = 0
  • Divide 9000 by 360: 9000 ÷ 360 : Remainder = 0
  • Divide 9000 by 375: 9000 ÷ 375 : Remainder = 0
  • Divide 9000 by 450: 9000 ÷ 450 : Remainder = 0
  • Divide 9000 by 500: 9000 ÷ 500 : Remainder = 0
  • Divide 9000 by 600: 9000 ÷ 600 : Remainder = 0
  • Divide 9000 by 750: 9000 ÷ 750 : Remainder = 0
  • Divide 9000 by 900: 9000 ÷ 900 : Remainder = 0
  • Divide 9000 by 1000: 9000 ÷ 1000 : Remainder = 0
  • Divide 9000 by 1125: 9000 ÷ 1125 : Remainder = 0
  • Divide 9000 by 1500: 9000 ÷ 1500 : Remainder = 0
  • Divide 9000 by 1800: 9000 ÷ 1800 : Remainder = 0
  • Divide 9000 by 2250: 9000 ÷ 2250 : Remainder = 0
  • Divide 9000 by 3000: 9000 ÷ 3000 : Remainder = 0
  • Divide 9000 by 4500: 9000 ÷ 4500 : Remainder = 0
  • Divide 9000 by 9000: 9000 ÷ 9000 : Remainder = 0

Hence, Factors of 9000 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 45, 50, 60, 72, 75, 90, 100, 120, 125, 150, 180, 200, 225, 250, 300, 360, 375, 450, 500, 600, 750, 900, 1000, 1125, 1500, 1800, 2250, 3000, 4500, and 9000

2. Steps to find factors of 9000 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

Method 1: Division Method

To find the primefactors of 9000 using the division method, follow these steps:

  • Step 1. Start dividing 9000 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
  • Step 2. After finding the smallest prime factor of the number 9000, which is 2. Divide 9000 by 2 to obtain the quotient (4500).
    9000 ÷ 2 = 4500
  • Step 3. Repeat step 1 with the obtained quotient (4500).
    4500 ÷ 2 = 2250
    2250 ÷ 2 = 1125
    1125 ÷ 3 = 375
    375 ÷ 3 = 125
    125 ÷ 5 = 25
    25 ÷ 5 = 5
    5 ÷ 5 = 1

So, the prime factorization of 9000 is, 9000 = 2 x 2 x 2 x 3 x 3 x 5 x 5 x 5.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 9000 as shown below:

So, the prime factorization of 9000 is, 9000 = 2 x 2 x 2 x 3 x 3 x 5 x 5 x 5.

3. Find factors of 9000 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 9000 would be the two numbers which, when multiplied, give 9000 as the result.

The following table represents the calculation of factors of 9000 in pairs:

Factor Pair Pair Factorization
1 and 9000 1 x 9000 = 9000
2 and 4500 2 x 4500 = 9000
3 and 3000 3 x 3000 = 9000
4 and 2250 4 x 2250 = 9000
5 and 1800 5 x 1800 = 9000
6 and 1500 6 x 1500 = 9000
8 and 1125 8 x 1125 = 9000
9 and 1000 9 x 1000 = 9000
10 and 900 10 x 900 = 9000
12 and 750 12 x 750 = 9000
15 and 600 15 x 600 = 9000
18 and 500 18 x 500 = 9000
20 and 450 20 x 450 = 9000
24 and 375 24 x 375 = 9000
25 and 360 25 x 360 = 9000
30 and 300 30 x 300 = 9000
36 and 250 36 x 250 = 9000
40 and 225 40 x 225 = 9000
45 and 200 45 x 200 = 9000
50 and 180 50 x 180 = 9000
60 and 150 60 x 150 = 9000
72 and 125 72 x 125 = 9000
75 and 120 75 x 120 = 9000
90 and 100 90 x 100 = 9000

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 9000. They are called negative pair factors.

Hence, the negative pairs of 9000 would be ( -1 , -9000 ) , ( -2 , -4500 ) , ( -3 , -3000 ) , ( -4 , -2250 ) , ( -5 , -1800 ) , ( -6 , -1500 ) , ( -8 , -1125 ) , ( -9 , -1000 ) , ( -10 , -900 ) , ( -12 , -750 ) , ( -15 , -600 ) , ( -18 , -500 ) , ( -20 , -450 ) , ( -24 , -375 ) , ( -25 , -360 ) , ( -30 , -300 ) , ( -36 , -250 ) , ( -40 , -225 ) , ( -45 , -200 ) , ( -50 , -180 ) , ( -60 , -150 ) , ( -72 , -125 ) , ( -75 , -120 ) and ( -90 , -100 ) .

What are factors?

In mathematics, a factor is that number which divides into another number exactly, without leaving a remainder. A factor of a number can be positive or negative.

Properties of factors

  • Each number is a factor of itself. Eg. 9000 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 9000.
  • Every number is a factor of zero (0), since 9000 x 0 = 0.
  • Every number other than 1 has at least two factors, namely the number itself and 1.
  • Every factor of a number is an exact divisor of that number, example 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 45, 50, 60, 72, 75, 90, 100, 120, 125, 150, 180, 200, 225, 250, 300, 360, 375, 450, 500, 600, 750, 900, 1000, 1125, 1500, 1800, 2250, 3000, 4500, 9000 are exact divisors of 9000.
  • Factors of 9000 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 45, 50, 60, 72, 75, 90, 100, 120, 125, 150, 180, 200, 225, 250, 300, 360, 375, 450, 500, 600, 750, 900, 1000, 1125, 1500, 1800, 2250, 3000, 4500, 9000. Each factor divides 9000 without leaving a remainder.
  • Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 45, 50, 60, 72, 75, 90, 100, 120, 125, 150, 180, 200, 225, 250, 300, 360, 375, 450, 500, 600, 750, 900, 1000, 1125, 1500, 1800, 2250, 3000, 4500, 9000 are all less than or equal to 9000.

Frequently Asked Questions

  • Which is the smallest prime factor of 9000?

    Smallest prime factor of 9000 is 2.

  • Is 9000 a perfect square?

    No 9000 is not a perfect square.

  • What are five multiples of 9000?

    First five multiples of 9000 are 18000, 27000, 36000, 45000, 54000.

  • What is prime factorization of 9000?

    Prime factorization of 9000 is 2 x 2 x 2 x 3 x 3 x 5 x 5 x 5.

  • What are factors of 9000?

    Factors of 9000 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 45, 50, 60, 72, 75, 90, 100, 120, 125, 150, 180, 200, 225, 250, 300, 360, 375, 450, 500, 600, 750, 900, 1000, 1125, 1500, 1800, 2250, 3000, 4500, 9000.

  • How do you find factors of a negative number? ( eg. -9000 )?

    Factors of -9000 are -1, -2, -3, -4, -5, -6, -8, -9, -10, -12, -15, -18, -20, -24, -25, -30, -36, -40, -45, -50, -60, -72, -75, -90, -100, -120, -125, -150, -180, -200, -225, -250, -300, -360, -375, -450, -500, -600, -750, -900, -1000, -1125, -1500, -1800, -2250, -3000, -4500, -9000.

  • Is 9000 a whole number?

    Yes 9000 is a whole number.

  • Which is greatest factor of 9000?

    The greatest factor of 9000 is 4500.

  • What are the prime factors of 9000?

    The factors of 9000 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 45, 50, 60, 72, 75, 90, 100, 120, 125, 150, 180, 200, 225, 250, 300, 360, 375, 450, 500, 600, 750, 900, 1000, 1125, 1500, 1800, 2250, 3000, 4500, 9000.
    Prime factors of 9000 are 2, 2, 2, 3, 3, 5, 5, 5.

Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 9000. Can you help her?

Prime factors of 9000 are 2, 2, 2, 3, 3, 5, 5, 5.
Hence, the product of prime factors of 30.

Can you help Rubel to find out the product of the even factors of 9000?

Factors of 9000 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 45, 50, 60, 72, 75, 90, 100, 120, 125, 150, 180, 200, 225, 250, 300, 360, 375, 450, 500, 600, 750, 900, 1000, 1125, 1500, 1800, 2250, 3000, 4500, 9000.
Even factors of 9000 are 2, 4, 6, 8, 10, 12, 18, 20, 24, 30, 36, 40, 50, 60, 72, 90, 100, 120, 150, 180, 200, 250, 300, 360, 450, 500, 600, 750, 900, 1000, 1500, 1800, 2250, 3000, 4500, 9000.
Hence, product of even factors of 9000 is; 2 x 4 x 6 x 8 x 10 x 12 x 18 x 20 x 24 x 30 x 36 x 40 x 50 x 60 x 72 x 90 x 100 x 120 x 150 x 180 x 200 x 250 x 300 x 360 x 450 x 500 x 600 x 750 x 900 x 1000 x 1500 x 1800 x 2250 x 3000 x 4500 x 9000 = 3.9346408075296526e+76.

Joy wants to calculate mean of all the factors of 9000. Help him in finding the mean of 9000.

Factors of 9000 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 45, 50, 60, 72, 75, 90, 100, 120, 125, 150, 180, 200, 225, 250, 300, 360, 375, 450, 500, 600, 750, 900, 1000, 1125, 1500, 1800, 2250, 3000, 4500, 9000.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 9000 is 1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 + 10 + 12 + 15 + 18 + 20 + 24 + 25 + 30 + 36 + 40 + 45 + 50 + 60 + 72 + 75 + 90 + 100 + 120 + 125 + 150 + 180 + 200 + 225 + 250 + 300 + 360 + 375 + 450 + 500 + 600 + 750 + 900 + 1000 + 1125 + 1500 + 1800 + 2250 + 3000 + 4500 + 9000 = 30420.
Hence, the mean of factors of 9000 is 30420 ÷ 48 = 633.75.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 9000? Help her in writing all the factors.

Positive factors are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 45, 50, 60, 72, 75, 90, 100, 120, 125, 150, 180, 200, 225, 250, 300, 360, 375, 450, 500, 600, 750, 900, 1000, 1125, 1500, 1800, 2250, 3000, 4500, 9000.
Negative factors are -1, -2, -3, -4, -5, -6, -8, -9, -10, -12, -15, -18, -20, -24, -25, -30, -36, -40, -45, -50, -60, -72, -75, -90, -100, -120, -125, -150, -180, -200, -225, -250, -300, -360, -375, -450, -500, -600, -750, -900, -1000, -1125, -1500, -1800, -2250, -3000, -4500, -9000.

How many factors are there for 9000?

Factors of 9000 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 45, 50, 60, 72, 75, 90, 100, 120, 125, 150, 180, 200, 225, 250, 300, 360, 375, 450, 500, 600, 750, 900, 1000, 1125, 1500, 1800, 2250, 3000, 4500, 9000.
So there are in total 48 factors.

Joey wants to write all the prime factors of 9000 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 9000 are 2, 2, 2, 3, 3, 5, 5, 5.
So in exponential form it can be written as 23 x 32 x 53.

Kevin has been asked to write 47 factor(s) of 9000. Can you predict the answer?

47 factor(s) of 9000 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 45, 50, 60, 72, 75, 90, 100, 120, 125, 150, 180, 200, 225, 250, 300, 360, 375, 450, 500, 600, 750, 900, 1000, 1125, 1500, 1800, 2250, 3000, 4500.