# Factors of 516 in pair

Factors of 516 in pair are (1, 516) , (2, 258) , (3, 172) , (4, 129) , (6, 86) and (12, 43)

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

 1.   Steps to find factors of 516 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 516 in pair

Factor Pair Pair Factorization
1 and 516 1 x 516 = 516
2 and 258 2 x 258 = 516
3 and 172 3 x 172 = 516
4 and 129 4 x 129 = 516
6 and 86 6 x 86 = 516
12 and 43 12 x 43 = 516

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 516. They are called negative pair factors.

Hence, the negative pairs of 516 would be ( -1 , -516 ) .

#### Introduction to factor pairs

Factor pair in mathematics is defined as all factors of a given number which when written in pair and multiplied gives the original number. Every natural number is a product of atleast one factor pair. Eg- Factors of 516 are 1 , 2 , 3 , 4 , 6 , 12 , 43 , 86 , 129 , 172 , 258 , 516. So, factors of 516 in pair are (1,516), (2,258), (3,172), (4,129), (6,86), (12,43).

#### How can we define factors?

In mathematics a factor is a number which divides into another without leaving any remainder. Or we can say, any two numbers that multiply to give a product are both factors of that product. It can be both positive or negative.

#### Properties of Factors

• Each number is a factor of itself. Eg. 516 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 516.
• Every number is a factor of zero (0), since 516 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, 43, 86, 129, 172, 258, 516 are exact divisors of 516.
• Factors of 516 are 1, 2, 3, 4, 6, 12, 43, 86, 129, 172, 258, 516. Each factor divides 516 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 12, 43, 86, 129, 172, 258, 516 are all less than or equal to 516.

#### Steps to find Factors of 516

• Step 1. Find all the numbers that would divide 516 without leaving any remainder. Starting with the number 1 upto 258 (half of 516). The number 1 and the number itself are always factors of the given number.
516 ÷ 1 : Remainder = 0
516 ÷ 2 : Remainder = 0
516 ÷ 3 : Remainder = 0
516 ÷ 4 : Remainder = 0
516 ÷ 6 : Remainder = 0
516 ÷ 12 : Remainder = 0
516 ÷ 43 : Remainder = 0
516 ÷ 86 : Remainder = 0
516 ÷ 129 : Remainder = 0
516 ÷ 172 : Remainder = 0
516 ÷ 258 : Remainder = 0
516 ÷ 516 : Remainder = 0

Hence, Factors of 516 are 1, 2, 3, 4, 6, 12, 43, 86, 129, 172, 258, and 516

• Is 516 a composite number?

Yes 516 is a composite number.

• Is 516 a prime number?

No 516 is not a prime number.

• What is the mean of factors of 516?

Factors of 516 are 1 , 2 , 3 , 4 , 6 , 12 , 43 , 86 , 129 , 172 , 258 , 516. therefore mean of factors of 516 is (1 + 2 + 3 + 4 + 6 + 12 + 43 + 86 + 129 + 172 + 258 + 516) / 12 = 102.67.

• 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.

#### Examples of Factors

Rustom has been assigned the following tasks by the teacher:
- Finding out all positive factors of 516.
- Writing all prime factors of 516.
- Writing all the possible factors of 516 in pair.
Help him in writing all these.

Positive factors of 516 are 1, 2, 3, 4, 6, 12, 43, 86, 129, 172, 258, 516.
Prime factors of 516 are 2, 2, 3, 43.
Factors of 516 in pair are (1,516), (2,258), (3,172), (4,129), (6,86), (12,43).

What are the pair factors of 516?

Factors of 516 are 1, 2, 3, 4, 6, 12, 43, 86, 129, 172, 258, 516. Hence, the factors of 516 in pair are (1,516), (2,258), (3,172), (4,129), (6,86), (12,43).

Can you help Sammy list the factors of 516 and also find the factor pairs?

Factors of 516 are 1, 2, 3, 4, 6, 12, 43, 86, 129, 172, 258, 516.
Factors of 516 in pair are (1,516), (2,258), (3,172), (4,129), (6,86), (12,43).

The area of a rectangle is 516 square meters. List all the possible combinations possible for length and breadth in which a designer can design out all the combinations.

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 516 in pair. So, the possible combinations (1,516), (2,258), (3,172), (4,129), (6,86), (12,43).

Help Diji in finding factors of 516 by Prime Factorization method and then sorting factors of 516 in pairs.

Prime factorization of 516 is 2 x 2 x 3 x 43. Factors of 516 in pair can be written as (1,516), (2,258), (3,172), (4,129), (6,86), (12,43).

Write the smallest prime factor of 516.

Smallest prime factor of 516 is 2.

Write the largest prime factor of 516.

Largest prime factor of 516 is 43.

Diji wants to write all the negative factors of 516. Can you help Diji in doing the same?

Negative factors of 516 are -1, -2, -3, -4, -6, -12, -43, -86, -129, -172, -258, -516.