# Factors of 312 in pair

Factors of 312 in pair are (1, 312) , (2, 156) , (3, 104) , (4, 78) , (6, 52) , (8, 39) , (12, 26) and (13, 24)

#### How to find factors of a number in pair

 1.   Steps to find factors of 312 in pair 2.   What is factors of a number in pair? 3.   What are Factors? 4.   Frequently Asked Questions 5.   Examples of factors in pair

### Example: Find factors of 312 in pair

Factor Pair Pair Factorization
1 and 312 1 x 312 = 312
2 and 156 2 x 156 = 312
3 and 104 3 x 104 = 312
4 and 78 4 x 78 = 312
6 and 52 6 x 52 = 312
8 and 39 8 x 39 = 312
12 and 26 12 x 26 = 312
13 and 24 13 x 24 = 312

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 312. They are called negative pair factors.

Hence, the negative pairs of 312 would be ( -1 , -312 ) .

#### How do you define factor pairs of a number?

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 312 are 1 , 2 , 3 , 4 , 6 , 8 , 12 , 13 , 24 , 26 , 39 , 52 , 78 , 104 , 156 , 312. So, factors of 312 in pair are (1,312), (2,156), (3,104), (4,78), (6,52), (8,39), (12,26), (13,24).

#### How do you explain factors?

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.

#### Properties of Factors

• Each number is a factor of itself. Eg. 312 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 312.
• Every number is a factor of zero (0), since 312 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, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312 are exact divisors of 312.
• Factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312. Each factor divides 312 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312 are all less than or equal to 312.

#### Steps to find Factors of 312

• Step 1. Find all the numbers that would divide 312 without leaving any remainder. Starting with the number 1 upto 156 (half of 312). The number 1 and the number itself are always factors of the given number.
312 ÷ 1 : Remainder = 0
312 ÷ 2 : Remainder = 0
312 ÷ 3 : Remainder = 0
312 ÷ 4 : Remainder = 0
312 ÷ 6 : Remainder = 0
312 ÷ 8 : Remainder = 0
312 ÷ 12 : Remainder = 0
312 ÷ 13 : Remainder = 0
312 ÷ 24 : Remainder = 0
312 ÷ 26 : Remainder = 0
312 ÷ 39 : Remainder = 0
312 ÷ 52 : Remainder = 0
312 ÷ 78 : Remainder = 0
312 ÷ 104 : Remainder = 0
312 ÷ 156 : Remainder = 0
312 ÷ 312 : Remainder = 0

Hence, Factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, and 312

• Is 312 a composite number?

Yes 312 is a composite number.

• Is 312 a prime number?

No 312 is not a prime number.

• What is the mean of factors of 312?

Factors of 312 are 1 , 2 , 3 , 4 , 6 , 8 , 12 , 13 , 24 , 26 , 39 , 52 , 78 , 104 , 156 , 312. therefore mean of factors of 312 is (1 + 2 + 3 + 4 + 6 + 8 + 12 + 13 + 24 + 26 + 39 + 52 + 78 + 104 + 156 + 312) / 16 = 52.50.

• 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 312 but she is finding it difficult. Can you help her find out?

Factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312. So, factors of 312 in pair are (1,312), (2,156), (3,104), (4,78), (6,52), (8,39), (12,26), (13,24).

Sammy wants to write all the negative factors of 312 in pair, but don't know how to start. Help Sammy in writing all the factor pairs.

Negative factors of 312 are -1, -2, -3, -4, -6, -8, -12, -13, -24, -26, -39, -52, -78, -104, -156, -312. Hence, factors of 312 in pair are (-1,-312), (-2,-156), (-3,-104), (-4,-78), (-6,-52), (-8,-39), (-12,-26), (-13,-24).

Help Deep in writing the positive factors of 312 in pair and negative factor of 312 in pair.

Factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312. Positive factors of 312 in pair are (1,312), (2,156), (3,104), (4,78), (6,52), (8,39), (12,26), (13,24). Negative factors of 312 in pair are (-1,-312), (-2,-156), (-3,-104), (-4,-78), (-6,-52), (-8,-39), (-12,-26), (-13,-24).

Find the product of all factors of 312.

Factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312. So the product of all factors of 312 would be 1 x 2 x 3 x 4 x 6 x 8 x 12 x 13 x 24 x 26 x 39 x 52 x 78 x 104 x 156 x 312 = 89791815397090000000.

Find the product of all prime factors of 312.

Factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312. Prime factors are 2, 2, 2, 3, 13. So, the product of all prime factors of 312 would be 2 x 2 x 2 x 3 x 13 = 312.

Can you help Sammy list the factors of 312 and also find the factor pairs?

Factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312.
Factors of 312 in pair are (1,312), (2,156), (3,104), (4,78), (6,52), (8,39), (12,26), (13,24).

Sammy has 312 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 312 blocks in all possible ways to form a rectangle, we need to calculate factors of 312 in pair. Therefore, factors of 312 in pair are (1,312), (2,156), (3,104), (4,78), (6,52), (8,39), (12,26), (13,24)