Factors Of 48

The factors are the numbers which give the original number when multiplied together. The factor of 48 can also be concluded by getting to know its multiplication factors. Also, we are going to derive here, the prime factors of 48.

The factor pairs are usually positive or negative whole numbers but not a fraction. The factor pair of 48 are also positive and negative whole numbers because two numbers with a negative sign if multiplied give a positive number. Thus, we can consider both positive and negative factors of a number. Finding the factors of a number is a very simple and easy method.

We usually start multiplying the original number with 1 and later with the multiplication of the pair of numbers coming in the sequence of whole numbers, whose multiplication will give the original number. The last pair will be the highest numbers which will give the original number after multiplication. Now, let us learn to find the factors of 48 in pairs.

Factor Pairs Of 48

We can find the factor of 48, by multiplying two numbers in a combination to get the result as 48. Let’s get started to find the factor pairs.

If 1 × 48 = 48, then (1, 48) is a factor pair of 48. Similarly, let us find other factor pairs of 48.

2 × 24 = 48; (2, 24) is a factor pair of 48

3 × 16 = 48; (3, 16) is a factor pair of 48

4 × 12 = 48; (4, 12) is a factor pair of 48

6 × 8 = 48; (6, 8) is a factor pair of 48

Therefore, the positive factor pairs of 48 are (1, 48), (2, 24), (3, 16), (4, 12) and (6, 8)

Similarly, if we have to find the negative factors of 48, then, we can write the multiples as;

-1 × -48 = 48; (-1, -48) is a factor pair of 48

-2 × -24 = 48; (-2, -24) is a factor pair of 48

-3 × -16 = 48; (-3, -16) is a factor pair of 48

-4 × -12 = 48; (-4, -12) is a factor pair of 48

-6 × -8 = 48; (-6, -8) is a factor pair of 48

Therefore, the negative factor pairs of 48 are (-1, -48), (-2, -24), (-3, -16), (-4, -12) and (-6, -8).

How to find the factors of 48?

You have known what are the factor pairs of 48 above. Now learn how to find factors of 48, step by step.

  • First, write the number 48.
  • Find the two numbers, which on multiplied gives 48, say 3 and 16, such as 3 × 16 = 48.
  • Now, factorize these numbers until they reach the prime number. We know, 3 is a prime number, but 16 have more factors such as 2 × 2 × 2 × 2 × 1.

    So, 48 = 3 × 2 × 2 × 2 × 2 × 1.

  • Write down all the unique numbers you will get after factorization.

Factors Of 48

1, 2, 3, 4, 6, 8, 12, 16, 24 and 48

Prime Factors of 48

The number 48 is a composite number. Now let us find the prime factor of 48.

  • The first step is to divide the number 48 with the smallest prime factor,i.e. 2.
  • 48 ÷ 2 = 24

  • Now, check whether 24 can be further divided by 2 or not.
  • 24 ÷ 2 = 12

    12 ÷ 2 = 6

    6 ÷ 2 = 3

  • As 3 cannot be divided by 2 because factors are the whole numbers and not the fraction.
  • Therefore, we need to divide 3 by 3 itself, as 3 is the next prime number.

    3 ÷ 3 = 1

  • We have received 1 at the end and further, we cannot proceed with the division method. So, the prime factors of 48 are 2 × 2 × 2 × 2 × 3 or we can also write them as 24 × 3, where 2 and 3 both are prime numbers.

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Practise This Question

Is it possible to construct a unique quadrilateral ABCD with AB = 5cm, BC = 6cm, CD= 7cm ,  ABC = 45 and  BCD = 55?