Factors of 720 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, and 720

How to find factors of a number

1. Steps to find factors of 720 using Division Method

Example: Find factors of 720

  • Divide 720 by 1: 720 ÷ 1 : Remainder = 0
  • Divide 720 by 2: 720 ÷ 2 : Remainder = 0
  • Divide 720 by 3: 720 ÷ 3 : Remainder = 0
  • Divide 720 by 4: 720 ÷ 4 : Remainder = 0
  • Divide 720 by 5: 720 ÷ 5 : Remainder = 0
  • Divide 720 by 6: 720 ÷ 6 : Remainder = 0
  • Divide 720 by 8: 720 ÷ 8 : Remainder = 0
  • Divide 720 by 9: 720 ÷ 9 : Remainder = 0
  • Divide 720 by 10: 720 ÷ 10 : Remainder = 0
  • Divide 720 by 12: 720 ÷ 12 : Remainder = 0
  • Divide 720 by 15: 720 ÷ 15 : Remainder = 0
  • Divide 720 by 16: 720 ÷ 16 : Remainder = 0
  • Divide 720 by 18: 720 ÷ 18 : Remainder = 0
  • Divide 720 by 20: 720 ÷ 20 : Remainder = 0
  • Divide 720 by 24: 720 ÷ 24 : Remainder = 0
  • Divide 720 by 30: 720 ÷ 30 : Remainder = 0
  • Divide 720 by 36: 720 ÷ 36 : Remainder = 0
  • Divide 720 by 40: 720 ÷ 40 : Remainder = 0
  • Divide 720 by 45: 720 ÷ 45 : Remainder = 0
  • Divide 720 by 48: 720 ÷ 48 : Remainder = 0
  • Divide 720 by 60: 720 ÷ 60 : Remainder = 0
  • Divide 720 by 72: 720 ÷ 72 : Remainder = 0
  • Divide 720 by 80: 720 ÷ 80 : Remainder = 0
  • Divide 720 by 90: 720 ÷ 90 : Remainder = 0
  • Divide 720 by 120: 720 ÷ 120 : Remainder = 0
  • Divide 720 by 144: 720 ÷ 144 : Remainder = 0
  • Divide 720 by 180: 720 ÷ 180 : Remainder = 0
  • Divide 720 by 240: 720 ÷ 240 : Remainder = 0
  • Divide 720 by 360: 720 ÷ 360 : Remainder = 0
  • Divide 720 by 720: 720 ÷ 720 : Remainder = 0

Hence, Factors of 720 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, and 720

2. Steps to find factors of 720 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 720 using the division method, follow these steps:

  • Step 1. Start dividing 720 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 720, which is 2. Divide 720 by 2 to obtain the quotient (360).
    720 ÷ 2 = 360
  • Step 3. Repeat step 1 with the obtained quotient (360).
    360 ÷ 2 = 180
    180 ÷ 2 = 90
    90 ÷ 2 = 45
    45 ÷ 3 = 15
    15 ÷ 3 = 5
    5 ÷ 5 = 1

So, the prime factorization of 720 is, 720 = 2 x 2 x 2 x 2 x 3 x 3 x 5.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 720 as shown below:

So, the prime factorization of 720 is, 720 = 2 x 2 x 2 x 2 x 3 x 3 x 5.

3. Find factors of 720 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 720 would be the two numbers which, when multiplied, give 720 as the result.

The following table represents the calculation of factors of 720 in pairs:

Factor Pair Pair Factorization
1 and 720 1 x 720 = 720
2 and 360 2 x 360 = 720
3 and 240 3 x 240 = 720
4 and 180 4 x 180 = 720
5 and 144 5 x 144 = 720
6 and 120 6 x 120 = 720
8 and 90 8 x 90 = 720
9 and 80 9 x 80 = 720
10 and 72 10 x 72 = 720
12 and 60 12 x 60 = 720
15 and 48 15 x 48 = 720
16 and 45 16 x 45 = 720
18 and 40 18 x 40 = 720
20 and 36 20 x 36 = 720
24 and 30 24 x 30 = 720

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 720. They are called negative pair factors.

Hence, the negative pairs of 720 would be ( -1 , -720 ) , ( -2 , -360 ) , ( -3 , -240 ) , ( -4 , -180 ) , ( -5 , -144 ) , ( -6 , -120 ) , ( -8 , -90 ) , ( -9 , -80 ) , ( -10 , -72 ) , ( -12 , -60 ) , ( -15 , -48 ) , ( -16 , -45 ) , ( -18 , -40 ) , ( -20 , -36 ) and ( -24 , -30 ) .

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. 720 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 720.
  • Every number is a factor of zero (0), since 720 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, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, 720 are exact divisors of 720.
  • Factors of 720 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, 720. Each factor divides 720 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, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, 720 are all less than or equal to 720.

Frequently Asked Questions

  • Which is the smallest prime factor of 720?

    Smallest prime factor of 720 is 2.

  • Is 720 a perfect square?

    No 720 is not a perfect square.

  • What are five multiples of 720?

    First five multiples of 720 are 1440, 2160, 2880, 3600, 4320.

  • What is prime factorization of 720?

    Prime factorization of 720 is 2 x 2 x 2 x 2 x 3 x 3 x 5.

  • What are factors of 720?

    Factors of 720 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, 720.

  • How do you find factors of a negative number? ( eg. -720 )?

    Factors of -720 are -1, -2, -3, -4, -5, -6, -8, -9, -10, -12, -15, -16, -18, -20, -24, -30, -36, -40, -45, -48, -60, -72, -80, -90, -120, -144, -180, -240, -360, -720.

  • Is 720 a whole number?

    Yes 720 is a whole number.

  • Which is greatest factor of 720?

    The greatest factor of 720 is 360.

  • What are the prime factors of 720?

    The factors of 720 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, 720.
    Prime factors of 720 are 2, 2, 2, 2, 3, 3, 5.

Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 720. Can you help her?

Prime factors of 720 are 2, 2, 2, 2, 3, 3, 5.
Hence, the product of prime factors of 30.

Can you help Rubel to find out the product of the even factors of 720?

Factors of 720 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, 720.
Even factors of 720 are 2, 4, 6, 8, 10, 12, 16, 18, 20, 24, 30, 36, 40, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, 720.
Hence, product of even factors of 720 is; 2 x 4 x 6 x 8 x 10 x 12 x 16 x 18 x 20 x 24 x 30 x 36 x 40 x 48 x 60 x 72 x 80 x 90 x 120 x 144 x 180 x 240 x 360 x 720 = 7.949684720339083e+37.

Joy wants to calculate mean of all the factors of 720. Help him in finding the mean of 720.

Factors of 720 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, 720.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 720 is 1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 + 10 + 12 + 15 + 16 + 18 + 20 + 24 + 30 + 36 + 40 + 45 + 48 + 60 + 72 + 80 + 90 + 120 + 144 + 180 + 240 + 360 + 720 = 2418.
Hence, the mean of factors of 720 is 2418 ÷ 30 = 80.60.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 720? Help her in writing all the factors.

Positive factors are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, 720.
Negative factors are -1, -2, -3, -4, -5, -6, -8, -9, -10, -12, -15, -16, -18, -20, -24, -30, -36, -40, -45, -48, -60, -72, -80, -90, -120, -144, -180, -240, -360, -720.

How many factors are there for 720?

Factors of 720 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, 720.
So there are in total 30 factors.

Joey wants to write all the prime factors of 720 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 720 are 2, 2, 2, 2, 3, 3, 5.
So in exponential form it can be written as 24 x 32 x 5.

Kevin has been asked to write 29 factor(s) of 720. Can you predict the answer?

29 factor(s) of 720 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360.