1. Steps to find factors of 60 using Division Method

Example: Find factors of 60

  • Divide 60 by 1: 60 ÷ 1 : Remainder = 0
  • Divide 60 by 2: 60 ÷ 2 : Remainder = 0
  • Divide 60 by 3: 60 ÷ 3 : Remainder = 0
  • Divide 60 by 4: 60 ÷ 4 : Remainder = 0
  • Divide 60 by 5: 60 ÷ 5 : Remainder = 0
  • Divide 60 by 6: 60 ÷ 6 : Remainder = 0
  • Divide 60 by 10: 60 ÷ 10 : Remainder = 0
  • Divide 60 by 12: 60 ÷ 12 : Remainder = 0
  • Divide 60 by 15: 60 ÷ 15 : Remainder = 0
  • Divide 60 by 20: 60 ÷ 20 : Remainder = 0
  • Divide 60 by 30: 60 ÷ 30 : Remainder = 0
  • Divide 60 by 60: 60 ÷ 60 : Remainder = 0

Hence, Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60

2. Steps to find factors of 60 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 60 using the division method, follow these steps:

  • Step 1. Start dividing 60 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 60, which is 2. Divide 60 by 2 to obtain the quotient (30).
    60 ÷ 2 = 30
  • Step 3. Repeat step 1 with the obtained quotient (30).
    30 ÷ 2 = 15
    15 ÷ 3 = 5
    5 ÷ 5 = 1

So, the prime factorization of 60 is, 60 = 2 x 2 x 3 x 5.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 60 as shown below:

So, the prime factorization of 60 is, 60 = 2 x 2 x 3 x 5.

3. Find factors of 60 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 60 would be the two numbers which, when multiplied, give 60 as the result.

The following table represents the calculation of factors of 60 in pairs:

Factor Pair Pair Factorization
1 and 60 1 x 60 = 60
2 and 30 2 x 30 = 60
3 and 20 3 x 20 = 60
4 and 15 4 x 15 = 60
5 and 12 5 x 12 = 60
6 and 10 6 x 10 = 60

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 60. They are called negative pair factors.

Hence, the negative pairs of 60 would be ( -1 , -60 ) , ( -2 , -30 ) , ( -3 , -20 ) , ( -4 , -15 ) , ( -5 , -12 ) and ( -6 , -10 ) .

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. 60 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 60.
  • Every number is a factor of zero (0), since 60 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, 10, 12, 15, 20, 30, 60 are exact divisors of 60.
  • Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. Each factor divides 60 without leaving a remainder.
  • Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 are all less than or equal to 60.

Frequently Asked Questions

  • How do you find factors of a negative number? ( eg. -60 )?

    Factors of -60 are -1, -2, -3, -4, -5, -6, -10, -12, -15, -20, -30, -60.

  • What is the sum of all factors of 60?

    The sum of all factors of 60 is 168.

  • What is prime factorization of 60?

    Prime factorization of 60 is 2 x 2 x 3 x 5.

  • What are the pair factors of 60?

    Pair factors of 60 are (1,60), (2,30), (3,20), (4,15), (5,12), (6,10).

  • What are six multiples of 60?

    First five multiples of 60 are 120, 180, 240, 300, 360, 420.

  • Is 60 a whole number?

    Yes 60 is a whole number.

  • Which is the smallest prime factor of 60?

    Smallest prime factor of 60 is 2.

  • What are five multiples of 60?

    First five multiples of 60 are 120, 180, 240, 300, 360.

  • Write all factors of 60?

    Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.

Examples of Factors

Joey wants to write all the prime factors of 60 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 60 are 2, 2, 3, 5.
So in exponential form it can be written as 22 x 3 x 5.

How many factors are there for 60?

Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
So there are in total 12 factors.

Kevin has been asked to write 11 factor(s) of 60. Can you predict the answer?

11 factor(s) of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30.

Sammy is puzzled while calculating the prime factors of 60. Can you help him find them?

Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
Prime factors of 60 are 2, 2, 3, 5

What is prime factorization of 60?

Prime factorization of 60 is 2 x 2 x 3 x 5 = 22 x 3 x 5.

Ariel has been assigned the task to find the product of all the prime factors of 60. Can you help her?

Prime factors of 60 are 2, 2, 3, 5.
Hence, the product of prime factors of 30.

Can you help Rubel to find out the product of the even factors of 60?

Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
Even factors of 60 are 2, 4, 6, 10, 12, 20, 30, 60.
Hence, product of even factors of 60 is; 2 x 4 x 6 x 10 x 12 x 20 x 30 x 60 = 207360000.