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

- 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.
- Pair the factors so that their product is 120, and read off the answer!

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 ) .

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).

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.

- 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.

**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 = 0120 ÷ 2 : Remainder = 0120 ÷ 3 : Remainder = 0120 ÷ 4 : Remainder = 0120 ÷ 5 : Remainder = 0120 ÷ 6 : Remainder = 0120 ÷ 8 : Remainder = 0120 ÷ 10 : Remainder = 0120 ÷ 12 : Remainder = 0120 ÷ 15 : Remainder = 0120 ÷ 20 : Remainder = 0120 ÷ 24 : Remainder = 0120 ÷ 30 : Remainder = 0120 ÷ 40 : Remainder = 0120 ÷ 60 : Remainder = 0120 ÷ 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**

**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.

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).

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).

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).

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.

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.

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).

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)