# Factors of 465 in pair

Factors of 465 in pair are (1, 465) , (3, 155) , (5, 93) and (15, 31)

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

 1.   Steps to find factors of 465 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 465 in pair

Factor Pair Pair Factorization
1 and 465 1 x 465 = 465
3 and 155 3 x 155 = 465
5 and 93 5 x 93 = 465
15 and 31 15 x 31 = 465

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 465. They are called negative pair factors.

Hence, the negative pairs of 465 would be ( -1 , -465 ) .

#### 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 465 are 1 , 3 , 5 , 15 , 31 , 93 , 155 , 465. So, factors of 465 in pair are (1,465), (3,155), (5,93), (15,31).

#### 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, 3, 5, 15, 31, 93, 155, 465 are exact divisors of 465.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 465 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 465.

#### Steps to find Factors of 465

• Step 1. Find all the numbers that would divide 465 without leaving any remainder. Starting with the number 1 upto 232 (half of 465). The number 1 and the number itself are always factors of the given number.
465 ÷ 1 : Remainder = 0
465 ÷ 3 : Remainder = 0
465 ÷ 5 : Remainder = 0
465 ÷ 15 : Remainder = 0
465 ÷ 31 : Remainder = 0
465 ÷ 93 : Remainder = 0
465 ÷ 155 : Remainder = 0
465 ÷ 465 : Remainder = 0

Hence, Factors of 465 are 1, 3, 5, 15, 31, 93, 155, and 465

• Is 465 a composite number?

Yes 465 is a composite number.

• Is 465 a perfect square?

No 465 is not a perfect square.

• Write all odd factors of 465?

The factors of 465 are 1, 3, 5, 15, 31, 93, 155, 465.
Odd factors of 465 are 1 , 3 , 5 , 15 , 31 , 93 , 155 , 465.

• What is the mean of all prime factors of 465?

Factors of 465 are 1 , 3 , 5 , 15 , 31 , 93 , 155 , 465. Prime factors of 465 are 3 , 5 , 31. Therefore mean of prime factors of 465 is (3 + 5 + 31) / 3 = 13.00.

• 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.

#### Examples of Factors

Can you help Rubel in arranging 465 blocks in order to form a rectangle in all possible ways? For arranging 465 blocks in order to form a rectangle in all possible ways we need to find factors of 465 in pair.

Factors of 465 are 1, 3, 5, 15, 31, 93, 155, 465. So, factors of 465 in pair are (1,465), (3,155), (5,93), (15,31).

How many total number of factors of 465 in pair are possible?

Factors of 465 are 1, 3, 5, 15, 31, 93, 155, 465. Hence, the factors of 465 in pair are (1,465), (3,155), (5,93), (15,31). Therefore, in total 4 pairs of factors are possible.

Sammy wants to write all the negative factors of 465 in pair, but don't know how to start. Help Sammy in writing all the factor pairs.

Negative factors of 465 are -1, -3, -5, -15, -31, -93, -155, -465. Hence, factors of 465 in pair are (-1,-465), (-3,-155), (-5,-93), (-15,-31).

Find the product of all prime factors of 465.

Factors of 465 are 1, 3, 5, 15, 31, 93, 155, 465. Prime factors are 3, 5, 31. So, the product of all prime factors of 465 would be 3 x 5 x 31 = 465.

A student has been assigned the following tasks by the teacher:
- Finding out all positive factors of 465.
- Writing all prime factors of 465.
- Writing all the possible factors of 465 in pair.
Help him in writing all these.

Positive factors of 465 are 1, 3, 5, 15, 31, 93, 155, 465.
Prime factors of 465 are 3, 5, 31.
Factors of 465 in pair are (1,465), (3,155), (5,93), (15,31).

Can you help Sammy list the factors of 465 and also find the factor pairs?

Factors of 465 are 1, 3, 5, 15, 31, 93, 155, 465.
Factors of 465 in pair are (1,465), (3,155), (5,93), (15,31).

Help Diji in finding factors of 465 by Prime Factorization method and then sorting factors of 465 in pairs.

Prime factorization of 465 is 3 x 5 x 31. Factors of 465 in pair can be written as (1,465), (3,155), (5,93), (15,31).

Write the smallest prime factor of 465.

Smallest prime factor of 465 is 3.