Factors of 228

Similarly, as we learned above, factors of 228 are such numbers that will be multiplied to get 228. There are both positive and negative factors of numbers that we will learn as we move ahead in the topic.

228 has only twelve factors: 1, 2, 3, 4, 6, 12, 19, 38, 57, 76, 114, and 228.

Negative factors of 228

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

Since 228 has twelve positive factors: 1, 2, 3, 4, 6, 12, 19, 38, 57, 76, 114, and 228, it will also have twelve negative counterparts:  -1, -2, -3, -4, -6, -12, -19, -38, -57, -76, -114, and -228.

Prime factors of 228: Since 228 is a composite number, it has 2, 3, and 19 as its prime factor.

Prime factorization of 228: Prime factorization of a number is the method of expressing 228 as a product of prime factors.

The prime factorization of 228 = 2² × 3¹× 19¹

There are several ways of finding factors of 228. 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 228 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 228.

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

Here, factor pairs of 228 are (1, 228), (2, 144), (3, 76), (4, 57), (6, 38), (8, 36), (12, 19).

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

In the method, we need to find such numbers that divide 228 completely without leaving any remainder.

228/1 = 228

228/ 2 = 89

228/ 3 = 76

228/ 4 = 57

228/ 6 = 38

228/ 12 = 19

228/ 19 = 12

228/ 38 = 6

228/ 57 = 4

228/ 76 = 3

228/ 114 = 2

228/ 228 = 1

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

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

Here, as we know, 228 = 2² × 3¹ × 19¹

 2, 3, and 19 are the prime factors when multiplied together will give 228 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 228 are (1, 228), (2, 245), (5, 98), (7, 70), (10, 49), and (14, 35)

Positive Pair Factors of 228 are  (1, 228), (2, 245), (5, 98), (7, 70), (10, 49), and (14, 35)

Negative Pair Factors of 228 are (-1, -228), (-2, -245), (-5, -98), (-7, -70), (-10, -49), and (-14, -35)

• 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.