Table of Contents
Factors of 54: Prime Factorization, Properties Factor Pairs
Factors of 54: Prime Factorization, Properties Factor Pairs: A factor is a number that divides another number by itself and leaves no remainder. In other words, if multiplying two whole numbers yields a product, the numbers being multiplied are factors of the result since the product is divisible by them.
There are two methods for determining factors: multiplication and prime factorization.
Example: Let us consider the number 15. 15 can be a product of 1 and 15, and 3 and 5. As a result, the factors of 15 are 1, 3, 5 and 15. As a result, only positive numbers, whole numbers, and non-fractional numbers are considered when finding or solving questions on factors.
Let’s learn about how to find the factors of a number in detail by taking the number 54 as an example.
Factors of 54
The numbers that can divide 54 exactly are known as factors of 54. When two factors are multiplied together to yield the number 54, they are referred to as pair factors.
Factors of 54 are 1,2,3,6,9,18,27 and 54
Pair Factors of 54
The number 54’s factor pairs are full numbers that are not fractions or decimal numbers. The factorization method will be used to identify the factors of a number, 54.
To obtain the pair factors, multiply the two integers in a pair to get the original number, 54, as shown below.
1 × 54 = 54
2 × 27 = 54
3 × 18 = 54
6 × 9 = 54
Therefore, the positive pair factors of 54 are (1, 54), (2, 27),(3, 18) and (6, 9).
Follow the steps below to find the negative pair factors of 54:
-1 × -54 = 54
-2 × -27 = 54
-3 × -18 = 54
-6 × -9 = 54
As a result, the negative pair factors of 54 are (-1, -54), (-2, -27), (-3, -18), and (-6, – 9).
Prime Factorization of 54
54 is a composite number that should have prime factors. Let us now see how to compute the prime factors of 54.
The first step is to divide 54 by the smallest prime factor, say 2, to get 27.
54 ÷ 2 = 27
Again, dividing 54 by 3 yields a fractional number that cannot be a factor, so proceed to the next prime factor, say 3
27 ÷ 3 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1
Finally, at the end of the prime factorization process, we get 1. As a result, we stop. Thus, the prime factors of 54 are 2 × 3 × 3 × 3 or 2x 3 3 , where 2 and 3 are prime numbers.
Some important properties of factors
● Any given number’s factor is its exact divisor.
● 1 is a factor for every number.
● The factor must always be less than or equal to the number.
● A number‘s greatest factor is the number itself.
Solved Examples
Q.1: There are 54 apples kept on a table. Harry has to distribute these apples equally to his three children. How many apples will each child get?
Ans: Number of apples = 54
Number of children = 3
Every kid will get = 54÷3 = 18 apples.
Q.2: What is the sum of all factors of 54?
Ans: The factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54.
When we add all of the factors together, we get;
1+2+3+6+9+18+27+54 = 120