Factors of 120 in pair are (1, 120) , (2, 60) , (3, 40) , (4, 30) , (5, 24) , (6, 20) , (8, 15) and (10, 12)

How to find factors of a number in pair

Steps to find factors of 120 in pair

Example: Find factors of 120 in pair

Factor Pair Pair Factorization
1 and 120 1 x 120 = 120
2 and 60 2 x 60 = 120
3 and 40 3 x 40 = 120
4 and 30 4 x 30 = 120
5 and 24 5 x 24 = 120
6 and 20 6 x 20 = 120
8 and 15 8 x 15 = 120
10 and 12 10 x 12 = 120

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 120. They are called negative pair factors.

Hence, the negative pairs of 120 would be ( -1 , -120 ) .

Definition of factor pairs?

In mathematics, factor pair are often given as pair of numbers which when multiplied together give the original number. Every natural number is a product of atleast one factor pair. Eg- Factors of 120 are 1 , 2 , 3 , 4 , 5 , 6 , 8 , 10 , 12 , 15 , 20 , 24 , 30 , 40 , 60 , 120. So, factors of 120 in pair are (1,120), (2,60), (3,40), (4,30), (5,24), (6,20), (8,15), (10,12).

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. 120 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 120.
  • Every number is a factor of zero (0), since 120 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, 10, 12, 15, 20, 24, 30, 40, 60, 120 are exact divisors of 120.
  • Factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120. Each factor divides 120 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, 10, 12, 15, 20, 24, 30, 40, 60, 120 are all less than or equal to 120.

Steps to find Factors of 120

  • Step 1. Find all the numbers that would divide 120 without leaving any remainder. Starting with the number 1 upto 60 (half of 120). The number 1 and the number itself are always factors of the given number.
    120 ÷ 1 : Remainder = 0
    120 ÷ 2 : Remainder = 0
    120 ÷ 3 : Remainder = 0
    120 ÷ 4 : Remainder = 0
    120 ÷ 5 : Remainder = 0
    120 ÷ 6 : Remainder = 0
    120 ÷ 8 : Remainder = 0
    120 ÷ 10 : Remainder = 0
    120 ÷ 12 : Remainder = 0
    120 ÷ 15 : Remainder = 0
    120 ÷ 20 : Remainder = 0
    120 ÷ 24 : Remainder = 0
    120 ÷ 30 : Remainder = 0
    120 ÷ 40 : Remainder = 0
    120 ÷ 60 : Remainder = 0
    120 ÷ 120 : Remainder = 0

Hence, Factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120

Frequently Asked Questions

  • Is 120 a composite number?

    Yes 120 is a composite number.

  • Is 120 a prime number?

    No 120 is not a prime number.

  • What is the mean of factors of 120?

    Factors of 120 are 1 , 2 , 3 , 4 , 5 , 6 , 8 , 10 , 12 , 15 , 20 , 24 , 30 , 40 , 60 , 120. therefore mean of factors of 120 is (1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 12 + 15 + 20 + 24 + 30 + 40 + 60 + 120) / 16 = 22.50.

  • What do you mean by proper divisors?

    A number x is said to be the proper divisor of y if it divides y completely, given that x is smaller than y.

  • What do you mean by improper divisors?

    An improper divisor of a number is the number itself apart from this any divisor of a given number is a proper divisor.

Examples of Factors

Ariel has been asked to write all factor pairs of 120 but she is finding it difficult. Can you help her find out?

Factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120. So, factors of 120 in pair are (1,120), (2,60), (3,40), (4,30), (5,24), (6,20), (8,15), (10,12).

Sammy wants to write all the negative factors of 120 in pair, but don't know how to start. Help Sammy in writing all the factor pairs.

Negative factors of 120 are -1, -2, -3, -4, -5, -6, -8, -10, -12, -15, -20, -24, -30, -40, -60, -120. Hence, factors of 120 in pair are (-1,-120), (-2,-60), (-3,-40), (-4,-30), (-5,-24), (-6,-20), (-8,-15), (-10,-12).

Help Deep in writing the positive factors of 120 in pair and negative factor of 120 in pair.

Factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120. Positive factors of 120 in pair are (1,120), (2,60), (3,40), (4,30), (5,24), (6,20), (8,15), (10,12). Negative factors of 120 in pair are (-1,-120), (-2,-60), (-3,-40), (-4,-30), (-5,-24), (-6,-20), (-8,-15), (-10,-12).

Find the product of all factors of 120.

Factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120. So the product of all factors of 120 would be 1 x 2 x 3 x 4 x 5 x 6 x 8 x 10 x 12 x 15 x 20 x 24 x 30 x 40 x 60 x 120 = 42998169600000000.

Find the product of all prime factors of 120.

Factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120. Prime factors are 2, 2, 2, 3, 5. So, the product of all prime factors of 120 would be 2 x 2 x 2 x 3 x 5 = 120.

Can you help Sammy list the factors of 120 and also find the factor pairs?

Factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120.
Factors of 120 in pair are (1,120), (2,60), (3,40), (4,30), (5,24), (6,20), (8,15), (10,12).

Sammy has 120 blocks and he wants to arrange them in all possible ways to form a rectangle but he doesn't know the technique for doing that, help Sammy in arrangements.

To arrange 120 blocks in all possible ways to form a rectangle, we need to calculate factors of 120 in pair. Therefore, factors of 120 in pair are (1,120), (2,60), (3,40), (4,30), (5,24), (6,20), (8,15), (10,12)