Factors of 12 in pair are (1, 12) , (2, 6) and (3, 4)

- Find all the numbers that would divide 12 without leaving any remainder. Starting with the number 1 upto 6 (half of 12). The number 1 and the number itself are always factors of the given number.
- Pair the factors so that their product is 12, and read off the answer!

Factor Pair | Pair Factorization |
---|---|

1 and 12 | 1 x 12 = 12 |

2 and 6 | 2 x 6 = 12 |

3 and 4 | 3 x 4 = 12 |

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 12. They are called negative pair factors.

Hence, the negative pairs of 12 would be ( -1 , -12 ) .

A factor pair of a number can be defined as the combination of two factors in such a way that when multiplied together produce the number itself. Every natural number is a product of atleast one factor pair. Eg- Factors of 12 are 1 , 2 , 3 , 4 , 6 , 12. So, factors of 12 in pair are (1,12), (2,6), (3,4).

In mathematics, a factor is a number or also it can be an algebraic expression that divides another number or any expression completely and that too without leaving any remainder. A factor of a number can be positive or negative.

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

**Step 1.**Find all the numbers that would divide 12 without leaving any remainder. Starting with the number 1 upto 6 (half of 12). The number 1 and the number itself are always factors of the given number.12 ÷ 1 : Remainder = 012 ÷ 2 : Remainder = 012 ÷ 3 : Remainder = 012 ÷ 4 : Remainder = 012 ÷ 6 : Remainder = 012 ÷ 12 : Remainder = 0

Hence, Factors of
*12* are **1, 2, 3, 4, 6, and 12**

**Is 12 a composite number?**Yes 12 is a composite number.

**Is 12 a prime number?**No 12 is not a prime number.

**What is the mean of factors of 12?**Factors of 12 are 1 , 2 , 3 , 4 , 6 , 12. therefore mean of factors of 12 is (1 + 2 + 3 + 4 + 6 + 12) / 6 = 4.67.

**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.

- Finding out all positive factors of 12.

- Writing all prime factors of 12.

- Writing all the possible factors of 12 in pair.

Help him in writing all these.

Positive factors of 12 are 1, 2, 3, 4, 6, 12.

Prime factors of 12 are 2, 2, 3.

Factors of 12 in pair are (1,12), (2,6), (3,4).

Factors of 12 are 1, 2, 3, 4, 6, 12. Hence, the factors of 12 in pair are (1,12), (2,6), (3,4).

Factors of 12 are 1, 2, 3, 4, 6, 12.

Factors of 12 in pair are (1,12), (2,6), (3,4).

For the possible combinations possible for length and breadth in which a designer can design out all the rectangles can be calculated by calculating the factors of 12 in pair. So, the possible combinations (1,12), (2,6), (3,4).

Prime factorization of 12 is 2 x 2 x 3. Factors of 12 in pair can be written as (1,12), (2,6), (3,4).

Smallest prime factor of 12 is 2.

Largest prime factor of 12 is 3.

Negative factors of 12 are -1, -2, -3, -4, -6, -12.