Factors of 4500 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 125, 150, 180, 225, 250, 300, 375, 450, 500, 750, 900, 1125, 1500, 2250, and 4500

How to find factors of a number

1. Steps to find factors of 4500 using Division Method

Example: Find factors of 4500

  • Divide 4500 by 1: 4500 ÷ 1 : Remainder = 0
  • Divide 4500 by 2: 4500 ÷ 2 : Remainder = 0
  • Divide 4500 by 3: 4500 ÷ 3 : Remainder = 0
  • Divide 4500 by 4: 4500 ÷ 4 : Remainder = 0
  • Divide 4500 by 5: 4500 ÷ 5 : Remainder = 0
  • Divide 4500 by 6: 4500 ÷ 6 : Remainder = 0
  • Divide 4500 by 9: 4500 ÷ 9 : Remainder = 0
  • Divide 4500 by 10: 4500 ÷ 10 : Remainder = 0
  • Divide 4500 by 12: 4500 ÷ 12 : Remainder = 0
  • Divide 4500 by 15: 4500 ÷ 15 : Remainder = 0
  • Divide 4500 by 18: 4500 ÷ 18 : Remainder = 0
  • Divide 4500 by 20: 4500 ÷ 20 : Remainder = 0
  • Divide 4500 by 25: 4500 ÷ 25 : Remainder = 0
  • Divide 4500 by 30: 4500 ÷ 30 : Remainder = 0
  • Divide 4500 by 36: 4500 ÷ 36 : Remainder = 0
  • Divide 4500 by 45: 4500 ÷ 45 : Remainder = 0
  • Divide 4500 by 50: 4500 ÷ 50 : Remainder = 0
  • Divide 4500 by 60: 4500 ÷ 60 : Remainder = 0
  • Divide 4500 by 75: 4500 ÷ 75 : Remainder = 0
  • Divide 4500 by 90: 4500 ÷ 90 : Remainder = 0
  • Divide 4500 by 100: 4500 ÷ 100 : Remainder = 0
  • Divide 4500 by 125: 4500 ÷ 125 : Remainder = 0
  • Divide 4500 by 150: 4500 ÷ 150 : Remainder = 0
  • Divide 4500 by 180: 4500 ÷ 180 : Remainder = 0
  • Divide 4500 by 225: 4500 ÷ 225 : Remainder = 0
  • Divide 4500 by 250: 4500 ÷ 250 : Remainder = 0
  • Divide 4500 by 300: 4500 ÷ 300 : Remainder = 0
  • Divide 4500 by 375: 4500 ÷ 375 : Remainder = 0
  • Divide 4500 by 450: 4500 ÷ 450 : Remainder = 0
  • Divide 4500 by 500: 4500 ÷ 500 : Remainder = 0
  • Divide 4500 by 750: 4500 ÷ 750 : Remainder = 0
  • Divide 4500 by 900: 4500 ÷ 900 : Remainder = 0
  • Divide 4500 by 1125: 4500 ÷ 1125 : Remainder = 0
  • Divide 4500 by 1500: 4500 ÷ 1500 : Remainder = 0
  • Divide 4500 by 2250: 4500 ÷ 2250 : Remainder = 0
  • Divide 4500 by 4500: 4500 ÷ 4500 : Remainder = 0

Hence, Factors of 4500 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 125, 150, 180, 225, 250, 300, 375, 450, 500, 750, 900, 1125, 1500, 2250, and 4500

2. Steps to find factors of 4500 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 4500 using the division method, follow these steps:

  • Step 1. Start dividing 4500 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 4500, which is 2. Divide 4500 by 2 to obtain the quotient (2250).
    4500 ÷ 2 = 2250
  • Step 3. Repeat step 1 with the obtained quotient (2250).
    2250 ÷ 2 = 1125
    1125 ÷ 3 = 375
    375 ÷ 3 = 125
    125 ÷ 5 = 25
    25 ÷ 5 = 5
    5 ÷ 5 = 1

So, the prime factorization of 4500 is, 4500 = 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 4500 as shown below:

So, the prime factorization of 4500 is, 4500 = 2 x 2 x 3 x 3 x 5 x 5 x 5.

3. Find factors of 4500 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 4500 would be the two numbers which, when multiplied, give 4500 as the result.

The following table represents the calculation of factors of 4500 in pairs:

Factor Pair Pair Factorization
1 and 4500 1 x 4500 = 4500
2 and 2250 2 x 2250 = 4500
3 and 1500 3 x 1500 = 4500
4 and 1125 4 x 1125 = 4500
5 and 900 5 x 900 = 4500
6 and 750 6 x 750 = 4500
9 and 500 9 x 500 = 4500
10 and 450 10 x 450 = 4500
12 and 375 12 x 375 = 4500
15 and 300 15 x 300 = 4500
18 and 250 18 x 250 = 4500
20 and 225 20 x 225 = 4500
25 and 180 25 x 180 = 4500
30 and 150 30 x 150 = 4500
36 and 125 36 x 125 = 4500
45 and 100 45 x 100 = 4500
50 and 90 50 x 90 = 4500
60 and 75 60 x 75 = 4500

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 4500. They are called negative pair factors.

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

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. 4500 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 4500.
  • Every number is a factor of zero (0), since 4500 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, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 125, 150, 180, 225, 250, 300, 375, 450, 500, 750, 900, 1125, 1500, 2250, 4500 are exact divisors of 4500.
  • Factors of 4500 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 125, 150, 180, 225, 250, 300, 375, 450, 500, 750, 900, 1125, 1500, 2250, 4500. Each factor divides 4500 without leaving a remainder.
  • Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 125, 150, 180, 225, 250, 300, 375, 450, 500, 750, 900, 1125, 1500, 2250, 4500 are all less than or equal to 4500.

Frequently Asked Questions

  • Which is the smallest prime factor of 4500?

    Smallest prime factor of 4500 is 2.

  • Is 4500 a perfect square?

    No 4500 is not a perfect square.

  • What are five multiples of 4500?

    First five multiples of 4500 are 9000, 13500, 18000, 22500, 27000.

  • What is prime factorization of 4500?

    Prime factorization of 4500 is 2 x 2 x 3 x 3 x 5 x 5 x 5.

  • What are factors of 4500?

    Factors of 4500 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 125, 150, 180, 225, 250, 300, 375, 450, 500, 750, 900, 1125, 1500, 2250, 4500.

  • How do you find factors of a negative number? ( eg. -4500 )?

    Factors of -4500 are -1, -2, -3, -4, -5, -6, -9, -10, -12, -15, -18, -20, -25, -30, -36, -45, -50, -60, -75, -90, -100, -125, -150, -180, -225, -250, -300, -375, -450, -500, -750, -900, -1125, -1500, -2250, -4500.

  • Is 4500 a whole number?

    Yes 4500 is a whole number.

  • Which is greatest factor of 4500?

    The greatest factor of 4500 is 2250.

  • What are the prime factors of 4500?

    The factors of 4500 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 125, 150, 180, 225, 250, 300, 375, 450, 500, 750, 900, 1125, 1500, 2250, 4500.
    Prime factors of 4500 are 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 4500. Can you help her?

Prime factors of 4500 are 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 4500?

Factors of 4500 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 125, 150, 180, 225, 250, 300, 375, 450, 500, 750, 900, 1125, 1500, 2250, 4500.
Even factors of 4500 are 2, 4, 6, 10, 12, 18, 20, 30, 36, 50, 60, 90, 100, 150, 180, 250, 300, 450, 500, 750, 900, 1500, 2250, 4500.
Hence, product of even factors of 4500 is; 2 x 4 x 6 x 10 x 12 x 18 x 20 x 30 x 36 x 50 x 60 x 90 x 100 x 150 x 180 x 250 x 300 x 450 x 500 x 750 x 900 x 1500 x 2250 x 4500 = 2.82429536481e+47.

Joy wants to calculate mean of all the factors of 4500. Help him in finding the mean of 4500.

Factors of 4500 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 125, 150, 180, 225, 250, 300, 375, 450, 500, 750, 900, 1125, 1500, 2250, 4500.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 4500 is 1 + 2 + 3 + 4 + 5 + 6 + 9 + 10 + 12 + 15 + 18 + 20 + 25 + 30 + 36 + 45 + 50 + 60 + 75 + 90 + 100 + 125 + 150 + 180 + 225 + 250 + 300 + 375 + 450 + 500 + 750 + 900 + 1125 + 1500 + 2250 + 4500 = 14196.
Hence, the mean of factors of 4500 is 14196 ÷ 36 = 394.33.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 4500? Help her in writing all the factors.

Positive factors are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 125, 150, 180, 225, 250, 300, 375, 450, 500, 750, 900, 1125, 1500, 2250, 4500.
Negative factors are -1, -2, -3, -4, -5, -6, -9, -10, -12, -15, -18, -20, -25, -30, -36, -45, -50, -60, -75, -90, -100, -125, -150, -180, -225, -250, -300, -375, -450, -500, -750, -900, -1125, -1500, -2250, -4500.

How many factors are there for 4500?

Factors of 4500 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 125, 150, 180, 225, 250, 300, 375, 450, 500, 750, 900, 1125, 1500, 2250, 4500.
So there are in total 36 factors.

Joey wants to write all the prime factors of 4500 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 4500 are 2, 2, 3, 3, 5, 5, 5.
So in exponential form it can be written as 22 x 32 x 53.

Kevin has been asked to write 35 factor(s) of 4500. Can you predict the answer?

35 factor(s) of 4500 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 125, 150, 180, 225, 250, 300, 375, 450, 500, 750, 900, 1125, 1500, 2250.