Factors of 456

Similarly, as we learned above, factors of 456 are such numbers that will be multiplied to get 456. There are both positive and negative factors of numbers that we will learn as we move ahead in the topic. 456 has only sixteen factors: 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456.
    

Negative factors of 456: Negative factors are nothing but the negative counterparts of the position factors of a number.

Since 456 has sixteen positive factors:  1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456, it will also have four negative counterparts, which are -1, -2, -3, -4, -6,  -8, -12, -19, -24, -38, -57, -76, -114, -152, -228, and -456.

Prime factors of 456:  Since 456 is a composite number, it has 2, 3, and 19 as its prime factor.

Prime factorization of 456: Prime factorization of a number is the method of expressing 456 as a product of prime factors.

The prime factorization of 456 = 2³× 3 × 19.
 

There are several ways of finding factors of 456. We will learn about them one by one as we go on.
 

In this method, we will try to find such a pair of numbers that will give 456 as their product. We recommend that you should follow the following steps to find factors using multiplication.

Step 1: Always look for a pair of numbers whose product is 456.

Step 2: After finding such pairs, list them all one by one.

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

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

In the method, we need to find such numbers that divide 456 completely without leaving any remainder.

456/1 = 456

456/ 2 = 89

456/ 3 = 128

456/ 4 = 96

456/ 8 = 48

456/ 12 = 32

456/ 19 = 24

456/ 24 = 16

456/ 38 = 12

456/ 57 = 8

456/ 76 = 6

456/ 114= 4

456/ 152 = 3

456/ 228 = 2

456/ 456 = 1

All the 16 numbers: 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, and 456, mentioned above divide 456 completely without any remainder. Hence, they are factors of 456.
 

In the prime factorization method, a number is expressed as the product of prime factors.

Here, as we know, 456 = 2³ × 3¹ × 19¹

 2, 3, and 19 are the prime factors when multiplied together will give 456 as a product of the multiplication.
 

A factor tree is a graphical representation of factors of any number. In the diagram, each branch represents the prime factors a number has.
 

The factor pairs of a number refer to a pair of numbers which, when multiplied, will give the number as a product.

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

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

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

• Prime Numbers: Those numbers which have no other factors other than 1 & the number itself.

• Composite Numbers: Those numbers that have more than 2 factors.

• Negative Factors: These are the counterparts of the positive factors of a number.

• Prime Factorization: Process of breaking down a composite number into products of several of its prime factors.