# Factors of 65 in pair

Factors of 65 in pair are (1, 65) , (5, 13)

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

 1.   Steps to find factors of 65 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 65 in pair

Factor Pair Pair Factorization
1 and 65 1 x 65 = 65
5 and 13 5 x 13 = 65

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 65. They are called negative pair factors.

Hence, the negative pairs of 65 would be ( -1 , -65 ) .

#### 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 65 are 1 , 5 , 13 , 65. So, factors of 65 in pair are (1,65), (5,13).

#### 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

• Every factor of a number is an exact divisor of that number, example 1, 5, 13, 65 are exact divisors of 65.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 65 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 65.

#### Steps to find Factors of 65

• Step 1. Find all the numbers that would divide 65 without leaving any remainder. Starting with the number 1 upto 32 (half of 65). The number 1 and the number itself are always factors of the given number.
65 ÷ 1 : Remainder = 0
65 ÷ 5 : Remainder = 0
65 ÷ 13 : Remainder = 0
65 ÷ 65 : Remainder = 0

Hence, Factors of 65 are 1, 5, 13, and 65

• Is 65 a perfect square?

No 65 is not a perfect square.

• Write five multiples of 65.

Five multiples of 65 are 130, 195, 260, 325, 390.

• Is there any even prime factor of 65?

No there is no even prime factor, i.e. 2, of 65.

• 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

Can you help Rubel in arranging 65 blocks in order to form a rectangle in all possible ways? For arranging 65 blocks in order to form a rectangle in all possible ways we need to find factors of 65 in pair.

Factors of 65 are 1, 5, 13, 65. So, factors of 65 in pair are (1,65), (5,13).

How many total number of factors of 65 in pair are possible?

Factors of 65 are 1, 5, 13, 65. Hence, the factors of 65 in pair are (1,65), (5,13). Therefore, in total 2 pairs of factors are possible.

Sammy wants to write all the negative factors of 65 in pair, but don't know how to start. Help Sammy in writing all the factor pairs.

Negative factors of 65 are -1, -5, -13, -65. Hence, factors of 65 in pair are (-1,-65), (-5,-13).

Find the product of all prime factors of 65.

Factors of 65 are 1, 5, 13, 65. Prime factors are 5, 13. So, the product of all prime factors of 65 would be 5 x 13 = 65.

A student has been assigned the following tasks by the teacher:
- Finding out all positive factors of 65.
- Writing all prime factors of 65.
- Writing all the possible factors of 65 in pair.
Help him in writing all these.

Positive factors of 65 are 1, 5, 13, 65.
Prime factors of 65 are 5, 13.
Factors of 65 in pair are (1,65), (5,13).

Can you help Sammy list the factors of 65 and also find the factor pairs?

Factors of 65 are 1, 5, 13, 65.
Factors of 65 in pair are (1,65), (5,13).

Help Diji in finding factors of 65 by Prime Factorization method and then sorting factors of 65 in pairs.

Prime factorization of 65 is 5 x 13. Factors of 65 in pair can be written as (1,65), (5,13).

Write the smallest prime factor of 65.

Smallest prime factor of 65 is 5.