# Factors of 456

Factors of 456 are 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, and 456

#### How to find factors of a number

 1.   Find factors of 456 using Division Method 2.   Find factors of 456 using Prime Factorization 3.   Find factors of 456 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 456

• Divide 456 by 1: 456 ÷ 1 : Remainder = 0
• Divide 456 by 2: 456 ÷ 2 : Remainder = 0
• Divide 456 by 3: 456 ÷ 3 : Remainder = 0
• Divide 456 by 4: 456 ÷ 4 : Remainder = 0
• Divide 456 by 6: 456 ÷ 6 : Remainder = 0
• Divide 456 by 8: 456 ÷ 8 : Remainder = 0
• Divide 456 by 12: 456 ÷ 12 : Remainder = 0
• Divide 456 by 19: 456 ÷ 19 : Remainder = 0
• Divide 456 by 24: 456 ÷ 24 : Remainder = 0
• Divide 456 by 38: 456 ÷ 38 : Remainder = 0
• Divide 456 by 57: 456 ÷ 57 : Remainder = 0
• Divide 456 by 76: 456 ÷ 76 : Remainder = 0
• Divide 456 by 114: 456 ÷ 114 : Remainder = 0
• Divide 456 by 152: 456 ÷ 152 : Remainder = 0
• Divide 456 by 228: 456 ÷ 228 : Remainder = 0
• Divide 456 by 456: 456 ÷ 456 : Remainder = 0

Hence, Factors of 456 are 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, and 456

#### 2. Steps to find factors of 456 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 456 using the division method, follow these steps:

• Step 1. Start dividing 456 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 456, which is 2. Divide 456 by 2 to obtain the quotient (228).
456 ÷ 2 = 228
• Step 3. Repeat step 1 with the obtained quotient (228).
228 ÷ 2 = 114
114 ÷ 2 = 57
57 ÷ 3 = 19
19 ÷ 19 = 1

So, the prime factorization of 456 is, 456 = 2 x 2 x 2 x 3 x 19.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 456 as shown below:

So, the prime factorization of 456 is, 456 = 2 x 2 x 2 x 3 x 19.

#### 3. Find factors of 456 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 456 would be the two numbers which, when multiplied, give 456 as the result.

The following table represents the calculation of factors of 456 in pairs:

Factor Pair Pair Factorization
1 and 456 1 x 456 = 456
2 and 228 2 x 228 = 456
3 and 152 3 x 152 = 456
4 and 114 4 x 114 = 456
6 and 76 6 x 76 = 456
8 and 57 8 x 57 = 456
12 and 38 12 x 38 = 456
19 and 24 19 x 24 = 456

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 456. They are called negative pair factors.

Hence, the negative pairs of 456 would be ( -1 , -456 ) , ( -2 , -228 ) , ( -3 , -152 ) , ( -4 , -114 ) , ( -6 , -76 ) , ( -8 , -57 ) , ( -12 , -38 ) and ( -19 , -24 ) .

#### 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. 456 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 456.
• Every number is a factor of zero (0), since 456 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, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456 are exact divisors of 456.
• Factors of 456 are 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456. Each factor divides 456 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456 are all less than or equal to 456.

• How do you find factors of a negative number? ( eg. -456 )?

Factors of -456 are -1, -2, -3, -4, -6, -8, -12, -19, -24, -38, -57, -76, -114, -152, -228, -456.

• What is the sum of all factors of 456?

The sum of all factors of 456 is 1200.

• What is prime factorization of 456?

Prime factorization of 456 is 2 x 2 x 2 x 3 x 19.

• What are the pair factors of 456?

Pair factors of 456 are (1,456), (2,228), (3,152), (4,114), (6,76), (8,57), (12,38), (19,24).

• What are six multiples of 456?

First five multiples of 456 are 912, 1368, 1824, 2280, 2736, 3192.

• Is 456 a whole number?

Yes 456 is a whole number.

• Which is the smallest prime factor of 456?

Smallest prime factor of 456 is 2.

• What are five multiples of 456?

First five multiples of 456 are 912, 1368, 1824, 2280, 2736.

• Write all factors of 456?

Factors of 456 are 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456.

#### Examples of Factors

Joey wants to write all the prime factors of 456 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 456 are 2, 2, 2, 3, 19.
So in exponential form it can be written as 23 x 3 x 19.

How many factors are there for 456?

Factors of 456 are 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456.
So there are in total 16 factors.

Kevin has been asked to write 15 factor(s) of 456. Can you predict the answer?

15 factor(s) of 456 are 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228.

Sammy is puzzled while calculating the prime factors of 456. Can you help him find them?

Factors of 456 are 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456.
Prime factors of 456 are 2, 2, 2, 3, 19

What is prime factorization of 456?

Prime factorization of 456 is 2 x 2 x 2 x 3 x 19 = 23 x 3 x 19.

Ariel has been assigned the task to find the product of all the prime factors of 456. Can you help her?

Prime factors of 456 are 2, 2, 2, 3, 19.
Hence, the product of prime factors of 114.

Can you help Rubel to find out the product of the even factors of 456?

Factors of 456 are 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456.
Even factors of 456 are 2, 4, 6, 8, 12, 24, 38, 76, 114, 152, 228, 456.
Hence, product of even factors of 456 is; 2 x 4 x 6 x 8 x 12 x 24 x 38 x 76 x 114 x 152 x 228 x 456 = 575398903529078800.