# Factors of 465

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

#### How to find factors of a number

 1.   Find factors of 465 using Division Method 2.   Find factors of 465 using Prime Factorization 3.   Find factors of 465 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 465

• Divide 465 by 1: 465 ÷ 1 : Remainder = 0
• Divide 465 by 3: 465 ÷ 3 : Remainder = 0
• Divide 465 by 5: 465 ÷ 5 : Remainder = 0
• Divide 465 by 15: 465 ÷ 15 : Remainder = 0
• Divide 465 by 31: 465 ÷ 31 : Remainder = 0
• Divide 465 by 93: 465 ÷ 93 : Remainder = 0
• Divide 465 by 155: 465 ÷ 155 : Remainder = 0
• Divide 465 by 465: 465 ÷ 465 : Remainder = 0

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

#### 2. Steps to find factors of 465 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

#### Method 1: Division Method

To find the primefactors of 465 using the division method, follow these steps:

• Step 1. Start dividing 465 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 465, which is 3. Divide 465 by 3 to obtain the quotient (155).
465 ÷ 3 = 155
• Step 3. Repeat step 1 with the obtained quotient (155).
155 ÷ 5 = 31
31 ÷ 31 = 1

So, the prime factorization of 465 is, 465 = 3 x 5 x 31.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 465 as shown below:

So, the prime factorization of 465 is, 465 = 3 x 5 x 31.

#### 3. Find factors of 465 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 465 would be the two numbers which, when multiplied, give 465 as the result.

The following table represents the calculation of factors of 465 in pairs:

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 ) , ( -3 , -155 ) , ( -5 , -93 ) and ( -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.

• How do you find factors of a negative number? ( eg. -465 )?

Factors of -465 are -1, -3, -5, -15, -31, -93, -155, -465.

• What is the sum of all factors of 465?

The sum of all factors of 465 is 768.

• What is prime factorization of 465?

Prime factorization of 465 is 3 x 5 x 31.

• What are the pair factors of 465?

Pair factors of 465 are (1,465), (3,155), (5,93), (15,31).

• What are six multiples of 465?

First five multiples of 465 are 930, 1395, 1860, 2325, 2790, 3255.

• Is 465 a whole number?

Yes 465 is a whole number.

• Which is the smallest prime factor of 465?

Smallest prime factor of 465 is 3.

• What are five multiples of 465?

First five multiples of 465 are 930, 1395, 1860, 2325, 2790.

• Write all factors of 465?

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

#### Examples of Factors

Joey wants to write all the prime factors of 465 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 465 are 3, 5, 31.
So in exponential form it can be written as 3 x 5 x 31.

How many factors are there for 465?

Factors of 465 are 1, 3, 5, 15, 31, 93, 155, 465.
So there are in total 8 factors.

Kevin has been asked to write 7 factor(s) of 465. Can you predict the answer?

7 factor(s) of 465 are 1, 3, 5, 15, 31, 93, 155.

Sammy is puzzled while calculating the prime factors of 465. Can you help him find them?

Factors of 465 are 1, 3, 5, 15, 31, 93, 155, 465.
Prime factors of 465 are 3, 5, 31

What is prime factorization of 465?

Prime factorization of 465 is 3 x 5 x 31 = 3 x 5 x 31.

Ariel has been assigned the task to find the product of all the prime factors of 465. Can you help her?

Prime factors of 465 are 3, 5, 31.
Hence, the product of prime factors of 465.

Can you help Rubel to find out the product of the even factors of 465?

Factors of 465 are 1, 3, 5, 15, 31, 93, 155, 465.
Even factors of 465 are 0.
Hence, product of even factors of 465 is; 0 = 0.