# Factors of 460

Factors of 460 are 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, and 460

#### How to find factors of a number

 1.   Find factors of 460 using Division Method 2.   Find factors of 460 using Prime Factorization 3.   Find factors of 460 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 460

• Divide 460 by 1: 460 ÷ 1 : Remainder = 0
• Divide 460 by 2: 460 ÷ 2 : Remainder = 0
• Divide 460 by 4: 460 ÷ 4 : Remainder = 0
• Divide 460 by 5: 460 ÷ 5 : Remainder = 0
• Divide 460 by 10: 460 ÷ 10 : Remainder = 0
• Divide 460 by 20: 460 ÷ 20 : Remainder = 0
• Divide 460 by 23: 460 ÷ 23 : Remainder = 0
• Divide 460 by 46: 460 ÷ 46 : Remainder = 0
• Divide 460 by 92: 460 ÷ 92 : Remainder = 0
• Divide 460 by 115: 460 ÷ 115 : Remainder = 0
• Divide 460 by 230: 460 ÷ 230 : Remainder = 0
• Divide 460 by 460: 460 ÷ 460 : Remainder = 0

Hence, Factors of 460 are 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, and 460

#### 2. Steps to find factors of 460 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 460 using the division method, follow these steps:

• Step 1. Start dividing 460 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 460, which is 2. Divide 460 by 2 to obtain the quotient (230).
460 ÷ 2 = 230
• Step 3. Repeat step 1 with the obtained quotient (230).
230 ÷ 2 = 115
115 ÷ 5 = 23
23 ÷ 23 = 1

So, the prime factorization of 460 is, 460 = 2 x 2 x 5 x 23.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 460 as shown below:

So, the prime factorization of 460 is, 460 = 2 x 2 x 5 x 23.

#### 3. Find factors of 460 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 460 would be the two numbers which, when multiplied, give 460 as the result.

The following table represents the calculation of factors of 460 in pairs:

Factor Pair Pair Factorization
1 and 460 1 x 460 = 460
2 and 230 2 x 230 = 460
4 and 115 4 x 115 = 460
5 and 92 5 x 92 = 460
10 and 46 10 x 46 = 460
20 and 23 20 x 23 = 460

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 460. They are called negative pair factors.

Hence, the negative pairs of 460 would be ( -1 , -460 ) , ( -2 , -230 ) , ( -4 , -115 ) , ( -5 , -92 ) , ( -10 , -46 ) and ( -20 , -23 ) .

#### 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

• Each number is a factor of itself. Eg. 460 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 460.
• Every number is a factor of zero (0), since 460 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, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460 are exact divisors of 460.
• Factors of 460 are 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460. Each factor divides 460 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460 are all less than or equal to 460.

• What are the prime factors of 460?

The factors of 460 are 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460.
Prime factors of 460 are 2, 2, 5, 23.

• What is the sum of all factors of 460?

The sum of all factors of 460 is 1008.

• What are the pair factors of 460?

Pair factors of 460 are (1,460), (2,230), (4,115), (5,92), (10,46), (20,23).

• What two numbers make 460?

Two numbers that make 460 are 2 and 230.

• What are multiples of 460?

First five multiples of 460 are 920, 1380, 1840, 2300.

• Is 460 a perfect square?

No 460 is not a perfect square.

• Which is greatest factor of 460?

The greatest factor of 460 is 230.

• How do you factors of 460?

Factors of 460 are 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460.

• What are five multiples of 460?

First five multiples of 460 are 920, 1380, 1840, 2300, 2760.

#### Examples of Factors

Can you help Rubel to find out the product of the even factors of 460?

Factors of 460 are 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460.
Even factors of 460 are 2, 4, 10, 20, 46, 92, 230, 460.
Hence, product of even factors of 460 is; 2 x 4 x 10 x 20 x 46 x 92 x 230 x 460 = 716392960000.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 460? Help her in writing all the factors.

Positive factors are 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460.
Negative factors are -1, -2, -4, -5, -10, -20, -23, -46, -92, -115, -230, -460.

How many factors are there for 460?

Factors of 460 are 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460.
So there are in total 12 factors.

Sammy is puzzled while calculating the prime factors of 460. Can you help him find them?

Factors of 460 are 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460.
Prime factors of 460 are 2, 2, 5, 23

Joey wants to write all the prime factors of 460 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 460 are 2, 2, 5, 23.
So in exponential form it can be written as 22 x 5 x 23.

What is prime factorization of 460?

Prime factorization of 460 is 2 x 2 x 5 x 23 = 22 x 5 x 23.

Can you help Rubel to find out the product of the even factors of 460?

Factors of 460 are 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460.
Even factors of 460 are 2, 4, 10, 20, 46, 92, 230, 460.
Hence, product of even factors of 460 is; 2 x 4 x 10 x 20 x 46 x 92 x 230 x 460 = 716392960000.