Factors of 1800 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, 150, 180, 200, 225, 300, 360, 450, 600, 900, and 1800

How to find factors of a number

1. Steps to find factors of 1800 using Division Method

Example: Find factors of 1800

  • Divide 1800 by 1: 1800 ÷ 1 : Remainder = 0
  • Divide 1800 by 2: 1800 ÷ 2 : Remainder = 0
  • Divide 1800 by 3: 1800 ÷ 3 : Remainder = 0
  • Divide 1800 by 4: 1800 ÷ 4 : Remainder = 0
  • Divide 1800 by 5: 1800 ÷ 5 : Remainder = 0
  • Divide 1800 by 6: 1800 ÷ 6 : Remainder = 0
  • Divide 1800 by 8: 1800 ÷ 8 : Remainder = 0
  • Divide 1800 by 9: 1800 ÷ 9 : Remainder = 0
  • Divide 1800 by 10: 1800 ÷ 10 : Remainder = 0
  • Divide 1800 by 12: 1800 ÷ 12 : Remainder = 0
  • Divide 1800 by 15: 1800 ÷ 15 : Remainder = 0
  • Divide 1800 by 18: 1800 ÷ 18 : Remainder = 0
  • Divide 1800 by 20: 1800 ÷ 20 : Remainder = 0
  • Divide 1800 by 24: 1800 ÷ 24 : Remainder = 0
  • Divide 1800 by 25: 1800 ÷ 25 : Remainder = 0
  • Divide 1800 by 30: 1800 ÷ 30 : Remainder = 0
  • Divide 1800 by 36: 1800 ÷ 36 : Remainder = 0
  • Divide 1800 by 40: 1800 ÷ 40 : Remainder = 0
  • Divide 1800 by 45: 1800 ÷ 45 : Remainder = 0
  • Divide 1800 by 50: 1800 ÷ 50 : Remainder = 0
  • Divide 1800 by 60: 1800 ÷ 60 : Remainder = 0
  • Divide 1800 by 72: 1800 ÷ 72 : Remainder = 0
  • Divide 1800 by 75: 1800 ÷ 75 : Remainder = 0
  • Divide 1800 by 90: 1800 ÷ 90 : Remainder = 0
  • Divide 1800 by 100: 1800 ÷ 100 : Remainder = 0
  • Divide 1800 by 120: 1800 ÷ 120 : Remainder = 0
  • Divide 1800 by 150: 1800 ÷ 150 : Remainder = 0
  • Divide 1800 by 180: 1800 ÷ 180 : Remainder = 0
  • Divide 1800 by 200: 1800 ÷ 200 : Remainder = 0
  • Divide 1800 by 225: 1800 ÷ 225 : Remainder = 0
  • Divide 1800 by 300: 1800 ÷ 300 : Remainder = 0
  • Divide 1800 by 360: 1800 ÷ 360 : Remainder = 0
  • Divide 1800 by 450: 1800 ÷ 450 : Remainder = 0
  • Divide 1800 by 600: 1800 ÷ 600 : Remainder = 0
  • Divide 1800 by 900: 1800 ÷ 900 : Remainder = 0
  • Divide 1800 by 1800: 1800 ÷ 1800 : Remainder = 0

Hence, Factors of 1800 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, 150, 180, 200, 225, 300, 360, 450, 600, 900, and 1800

2. Steps to find factors of 1800 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 1800 using the division method, follow these steps:

  • Step 1. Start dividing 1800 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 1800, which is 2. Divide 1800 by 2 to obtain the quotient (900).
    1800 ÷ 2 = 900
  • Step 3. Repeat step 1 with the obtained quotient (900).
    900 ÷ 2 = 450
    450 ÷ 2 = 225
    225 ÷ 3 = 75
    75 ÷ 3 = 25
    25 ÷ 5 = 5
    5 ÷ 5 = 1

So, the prime factorization of 1800 is, 1800 = 2 x 2 x 2 x 3 x 3 x 5 x 5.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 1800 as shown below:

So, the prime factorization of 1800 is, 1800 = 2 x 2 x 2 x 3 x 3 x 5 x 5.

3. Find factors of 1800 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 1800 would be the two numbers which, when multiplied, give 1800 as the result.

The following table represents the calculation of factors of 1800 in pairs:

Factor Pair Pair Factorization
1 and 1800 1 x 1800 = 1800
2 and 900 2 x 900 = 1800
3 and 600 3 x 600 = 1800
4 and 450 4 x 450 = 1800
5 and 360 5 x 360 = 1800
6 and 300 6 x 300 = 1800
8 and 225 8 x 225 = 1800
9 and 200 9 x 200 = 1800
10 and 180 10 x 180 = 1800
12 and 150 12 x 150 = 1800
15 and 120 15 x 120 = 1800
18 and 100 18 x 100 = 1800
20 and 90 20 x 90 = 1800
24 and 75 24 x 75 = 1800
25 and 72 25 x 72 = 1800
30 and 60 30 x 60 = 1800
36 and 50 36 x 50 = 1800
40 and 45 40 x 45 = 1800

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 1800. They are called negative pair factors.

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

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. 1800 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 1800.
  • Every number is a factor of zero (0), since 1800 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, 150, 180, 200, 225, 300, 360, 450, 600, 900, 1800 are exact divisors of 1800.
  • Factors of 1800 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, 150, 180, 200, 225, 300, 360, 450, 600, 900, 1800. Each factor divides 1800 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, 150, 180, 200, 225, 300, 360, 450, 600, 900, 1800 are all less than or equal to 1800.

Frequently Asked Questions

  • Which is the smallest prime factor of 1800?

    Smallest prime factor of 1800 is 2.

  • Is 1800 a perfect square?

    No 1800 is not a perfect square.

  • What are five multiples of 1800?

    First five multiples of 1800 are 3600, 5400, 7200, 9000, 10800.

  • What is prime factorization of 1800?

    Prime factorization of 1800 is 2 x 2 x 2 x 3 x 3 x 5 x 5.

  • What are factors of 1800?

    Factors of 1800 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, 150, 180, 200, 225, 300, 360, 450, 600, 900, 1800.

  • How do you find factors of a negative number? ( eg. -1800 )?

    Factors of -1800 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, -150, -180, -200, -225, -300, -360, -450, -600, -900, -1800.

  • Is 1800 a whole number?

    Yes 1800 is a whole number.

  • Which is greatest factor of 1800?

    The greatest factor of 1800 is 900.

  • What are the prime factors of 1800?

    The factors of 1800 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, 150, 180, 200, 225, 300, 360, 450, 600, 900, 1800.
    Prime factors of 1800 are 2, 2, 2, 3, 3, 5, 5.

Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 1800. Can you help her?

Prime factors of 1800 are 2, 2, 2, 3, 3, 5, 5.
Hence, the product of prime factors of 30.

Can you help Rubel to find out the product of the even factors of 1800?

Factors of 1800 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, 150, 180, 200, 225, 300, 360, 450, 600, 900, 1800.
Even factors of 1800 are 2, 4, 6, 8, 10, 12, 18, 20, 24, 30, 36, 40, 50, 60, 72, 90, 100, 120, 150, 180, 200, 300, 360, 450, 600, 900, 1800.
Hence, product of even factors of 1800 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 300 x 360 x 450 x 600 x 900 x 1800 = 1.0234903690774693e+48.

Joy wants to calculate mean of all the factors of 1800. Help him in finding the mean of 1800.

Factors of 1800 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, 150, 180, 200, 225, 300, 360, 450, 600, 900, 1800.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 1800 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 + 150 + 180 + 200 + 225 + 300 + 360 + 450 + 600 + 900 + 1800 = 6045.
Hence, the mean of factors of 1800 is 6045 ÷ 36 = 167.92.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 1800? 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, 150, 180, 200, 225, 300, 360, 450, 600, 900, 1800.
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, -150, -180, -200, -225, -300, -360, -450, -600, -900, -1800.

How many factors are there for 1800?

Factors of 1800 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, 150, 180, 200, 225, 300, 360, 450, 600, 900, 1800.
So there are in total 36 factors.

Joey wants to write all the prime factors of 1800 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 1800 are 2, 2, 2, 3, 3, 5, 5.
So in exponential form it can be written as 23 x 32 x 52.

Kevin has been asked to write 35 factor(s) of 1800. Can you predict the answer?

35 factor(s) of 1800 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, 150, 180, 200, 225, 300, 360, 450, 600, 900.