Know How to Easily Find Factors of 24 and 42

A factor in mathematics is a divisor of a given integer that divides it completely without leaving any remainder. A factor is a number that completely divides another number without leaving any remainder. We come across factors and multiples all the time. They are used to, among other things, organising goods in a box, handling money, recognising patterns in numbers, solving ratios, and working with expanding or reducing fractions.

 

In mathematics, factorization or factoring is the process of representing a number as a product of many factors. For example, 4 × 8 is a factorization of the integer 42 and (6,7) are factors of 42.

 

Let’s learn about the factorization of a number properly by taking two numbers 24 and 42 as examples.

Factors of 24

Factors of 24 are integers that divide 24 completely without leaving any remainder. There are eight 24 factors, with 24 being the largest and the prime factors being 2 and 3.

How to Find the Factors of 24?

When a number is written as a product of its factors, it is factorised. The multiplication method is the most commonly used method for calculating a number's factors. Let's use the multiplication method to discover the factors of 24.

Pair Factors of 24

By multiplying two integers in a pair to get the original number as 24, we may get the factors of the number 24.

 

1 × 24 = 24

2 × 12 = 24

3 × 8 = 24

4 × 6 = 24

 

Thus, the pair factors of 24 are (1, 24), (2, 12), (3, 8), and (4, 6).

Prime Factorisation of 24

The number 24 is made up of several factors. Let us now look for the prime factors of 24.

 

●      The first step is to divide 24 by the smallest prime factor, which is 2. 24 ÷ 2 = 12

 

Again, divide 12 by 2.

 

12 ÷ 2 = 6

6 ÷ 2 = 3

 

●      Now, dividing 3 by 2 yields a fraction number that cannot be a factor.

 

●      Now move on to the next prime number, which is 3.

3 ÷ 3 = 1

 

●      We received 1 at the end, therefore we can't use the division method anymore. As a result, the prime factorisation of 24 is  2 × 2 × 2 × 3 or 2³ × 3, where 2 and 3 are prime numbers.

What are the Factors of 42?

Factors of 42 are numbers that divide 42 exactly without a remainder. Because 42 is a composite number, it has many factors other than one and the number itself. 42 factors can be positive or negative, but they cannot be expressed in decimal or fraction form. The factors of 42 are thus 1, 2, 3, 6, 7, 14, 21, and 42.

Pair Factors of 42

We can determine the factors in pairs for 42 by multiplying two integers in a combination to get the result 42. To accomplish this, take the following steps:

 

1 × 42 = 42

 

2 × 21 = 42

 

3 × 14 = 42

 

6 × 7 = 42

 

As a result, the factors of 42 in pairs are (1, 42), (2, 21), (3, 14),  (4, 14) and (6, 7).

Prime Factorization of 42

The number 42 is composed of several factors. Let us now look for the prime factors of 42.

 

●      To begin, divide 42 by the smallest prime factor, which is 2.

 

42 ÷ 2 = 21

 

●      Check whether 21 can be divided by two, one more times.

 

21÷2= 10.5

 

In contrast, a factor cannot be a fraction. As a result, we'll proceed to the next prime number, three.

 

●      Now, dividing 21 by 3 yields

 

21 ÷ 3 = 7

 

●      Divide 7 by 3 once more to get a fraction number. As a result, consider the next prime number, 5.

 

Again, a fraction: 21÷5 = 4.2.

 

As a result, 7 is the next prime number.

 

7 ÷ 7 = 1

 

●      We have 1 at the end, and we can't utilise the division method because the factor of 1 is only 1. Therefore, we can say the prime factors of 42 are 2, 3 and 7.