Factors of 420 | Prime factors of 420 with a Detailed Explanation (2024)

The factors of 420 are the numbers which get multiplied and produce the result as 420. For example, multiplying 5 and 7, we get 35, i.e. 5 × 7 = 35 such that 5 and 7 are the factors of 35. Also, (5, 7) is called one of the factor pairs of 35. In the same way, we can find the factors of the number 420. In this article, you will know the factors of 420, how to find the factors of a number 420 in pairs and prime factors of 420 with detailed steps.

What are the Factors of 420?

Also, we know that the factors of 420 are the exact divisors of that number. The number 420 is a composite number and hence it has more than two factors, that means it has factors other than 1 and 420.

However, we can find the factors for any given number in two ways, namely division method and factor pair method.

How to Find the Factors of 420?

Go through the steps given below to understanding the process of finding the factors of 420.

Step 1: First, write the number 420 in your notebook.

Step 2: Find the two numbers, which on multiplication gives 420, suppose 2 and 210, such as 2 × 210 = 420.

Step 3: We know that 2 is a prime number which has only two factors, i.e. 1 and the number itself. So, we cannot factorize it further.

2 = 1 × 2

Step 4: Now, let’s try with different combinations of numbers in multiplication that produce the result as 420, such as

3 × 140 = 420

4 × 105 = 420

5 × 84 = 420 and so on.

Step 5: Therefore, factors of 420 are: 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20 , 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210 and 420.

As we know, factors are the exact divisors of the numbers. So we can also find the factors for 420 by the division method.

420 ÷ 1 = 420 {remainder = 0, 1 and 420 are factors}

420 ÷ 2 = 210 {remainder = 0, 2 and 210 are factors}

420 ÷ 3 = 140 {remainder = 0, 3 and 140 are factors}

420 ÷ 4 = 105 {remainder = 0, 4 and 105 are factors}

420 ÷ 5 = 84 {remainder = 0, 5 and 84 are factors}

420 ÷ 6 = 70 {remainder = 0, 6 and 70 are factors}

420 ÷ 7 = 60 {remainder = 0, 7 and 60 are factors}

420 ÷ 10 = 42 {remainder = 0, 10 and 42 are factors}

420 ÷ 12 = 35 {remainder = 0, 12 and 35 are factors}

420 ÷ 14 = 30 {remainder = 0, 14 and 30 are factors}

420 ÷ 15 = 28 {remainder = 0, 15 and 28 are factors}

420 ÷ 20 = 21 {remainder = 0, 20 and 21 are factors}

420 ÷ 21 = 20 {remainder = 0, 21 and 20 are factors}

Factor of 420 in Pairs

The factors of any number can be both positive and negative. To find the pair factors of 420, multiply the 2 numbers in a pair to have the original number as 420. Such numbers are tabulated below:

Similarly, we can write other pair factors by interchanging the numbers within the pair, such as (28, 15), (30, 14), and so on.

How to calculate Prime Factors of 420?

By prime factorization method, we can write the prime factors of 420 as given below.

Step 1: The first step is to divide the number 420 with the smallest prime number, i.e. 2.

420 ÷ 2 = 210

2 is a prime factor of 420

Step 2: Now, we divide 210 by 2.

210 ÷ 2 = 105; again 2 is a prime factor.

Step 3: Divide 105 by 2.

105 ÷ 2 = 52.5

As we know, the factors cannot be a fraction, therefore, 2 is not the prime factor for 105.

Step 4: Now, proceed to the next prime numbers, i.e. 3, 5, 7 and so on.

105 ÷ 3 = 35; 3 is one of the prime factors.

Step 5: Let’s divide 35.

35 ÷ 2 = 17.5; not a prime factor

35 ÷ 3 = 11.6667; not a prime factor. So proceed with the next numbers.

35 ÷ 5 = 7; a prime factor

Step 6: Divide 7 as:

7 ÷ 2 = 3.5

7 ÷ 3 = 2.33

7 ÷ 5 = 1.4

7 ÷ 7 = 1

Finally, we received 1 in the above process. Hence, we cannot proceed with the division method.

Thus, the prime factorisation of 420 can be expressed as 2 × 2 × 3 × 5 × 7.

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