Factorisation of Numbers like 54 and 32 in Detail

Learn Factorisation of Numbers like 54 and 32 in Detail

How to find the Factors using Different Methods with Solved Example :-

Whole numbers that are multiplied together to form another number are referred to as factors. If a × b = c, then a and b are the factors of c.

Say you wanted to find the factors of 54. You would find all pairs of numbers that when multiplied together resulted in 54. We know 2 and 27 are factors of 54 because 2 × 27 = 54. Also, 1 and 54 are factors of 54 because 1 × 54 = 54. In the same way, you can find all factors of 15, which are 1,2,3,6,9,18,27 and 54.

Learn-Factorisation-of-Numbers-like-54-and-32-in-Detail
Factorisation of Numbers like 54 and 32 in Detail

You can also think about factors in the terms of division: The factors of a number include all numbers that divide evenly into that number, basically leaving no remainder. Consider the number 12. Since 12 is evenly divisible by 2 and 6, you can conclude that both 2 and 6 are the factors of 12.

Factor of 32

Factors of 32 are integers that can be divided evenly into 32. It consists of six factors: 1, 2, 4, 8, 16, and 32. Since any integer is a factor of itself, 32 is also a factor of itself.

Factors Pairs of 32

 The two numbers that multiply to give 32 are the factor pairs of 32. The factors pairs of 32 are listed in pairs below.

Positive Pair Factors

1 × 32 = 32

2 × 16 = 32

4 × 8 = 32

Therefore, the negative factor pairs of 32 are (1, 32), (2, 16) and (4, 8).

Negative Pair Factors

-1 × -32 = 32

-2 × -16 = 32

-4 × -8 = 32

Therefore, the positive factor pairs of 32 are (-1, -32), (-2, -16) and (-4, -8).

Prime Factors of 32

As we’ve seen with the factors of 32, the only prime factor it includes is 2. Prime factors are numbers that can only be divided by one and themselves. Again, the number one is neither composite nor prime. 2 is the smallest prime number. The next prime number greater than two is three.

The prime factorization of 32 is 2*2*2*2*2*2, which equals 25.

Factors of 54

Factors of 54 are numbers that can divide 54 perfectly. Pair factors occur when two factors are multiplied together to produce the number 54.

The factors of 54 are 1,2,3,6,9,18,27, and 54.

To find the factors of a number, 54, we will use the pair factor and prime factorization method.

Pair Factors of 54

The factor pairs of 54 are full numbers that are not fractions or decimal numbers.

To obtain the pair factors, multiply the two integers in a pair to get the original number, 54, as shown below.

1×54 = 54, (1, 54) is a 54 pair factor.

2×27 = 54, which is a pair factor of 54.

3×18 = 54, (3, 18) is a 54 pair factor.

6×9 = 54, which is a pair factor of 54.

As a result, the positive pair factors are (1, 54), (2, 27), (3, 18), (3, 18) and (6, 9).

Prime Factors 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 quotient 1. As a result, we are done. Thus, the prime factors of 54 are 2 × 3 × 3 × 3 or 2x 33, where 2 and 3 are the prime numbers.

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