 # Factors Of 63

Factors of 60 are the numbers which when multiplied in pairs results in the original number. We can also say that, when 60 is divided by any of its factors, then the resulted quotient is a whole number. 60 is a composite number, so it has factors of more than 2. Similarly, factors of 72, 60, 56, 35, 81, etc. will have more than two numbers. To find the factors of number 63, we will use the division method here. In this article, we are going to learn the factors of 63, pair factors and the prime factors of 63 using the prime factorization method and many solved examples.

## What are the Factors of 63?

The factors of 63 are the numbers that divide the number 63 exactly without leaving any remainder. In other words, the factors of 63 are the numbers that are multiplied in pairs resulting in the original number 63. Since the number 63 is a composite number, 63 has more than two factors. Thus, the factors of 63 are 1, 3, 7, 9, 21 and 63.

 Factors of 63: 1, 3, 7, 9, 21 and 63 Prime Factorization of 63: 3 × 3 × 7 or 32 × 7

## Pair Factors of 63

The pair factors of 63 are the numbers that are multiplied in pairs to give the product value as 63. As the factors of 63 can be positive or negative, the pair factors of 63 can also be positive or negative, but they cannot be in fraction or decimal form. Thus, the positive and negative pair factors of 63 are given below.

Positive Pair Factors of 63:

 Positive Factors of 63 Positive Pair Factors of 63 1 × 63 (1, 63) 3 × 21 (3, 21) 7 × 9 (7, 9)

Negative Pair Factors of 63:

 Negative Factors of 63 Negative Pair Factors of 63 -1 ×- 63 (-1, -63) -3 × -21 (-3, -21) -7 × -9 (-7, -9)

### Prime Factorization of 63

The number 63 is a composite number. Now let us find the prime factors associated with 63.

• The first step is to divide the number 63 with the smallest prime factor,i.e. 2.

63 ÷ 2 = 31.5; fraction cannot be a factor. Therefore, moving to the next prime number

Divide 63 by 3.

63 ÷ 3 = 21

• Again divide 21 by 3 and keep on diving the output by 3 till you get 1 or a fraction.

21 ÷ 3 = 7

7 ÷ 3 = 2.33; cannot be a factor. Now move to the next prime number 7.

• Dividing 7 by 7 we get,

7 ÷ 7 = 1

• We have received 1 at the end and it doesn’t have any factor. Therefore, we cannot proceed further with the division method. So, the prime factorisation of 63 is 3 × 3 × 7 or 32 × 7, where 3 and 7 are the prime numbers.
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### Examples

Example 1:

Find the common factors of 63 and 62.

Solution:

The factors of 63 are 1, 3, 7, 9, 21 and 63

The factors of 62 are 1, 2, 31, 62.

Thus, the common factor of 63 and 62 is 1.

Example 2:

Find the common factors of 63 and 64.

Solution:

Factors of 63 = 1, 3, 7, 9, 21 and 63

Factors of 64 = 1, 2, 4, 8, 16, 32 and 64

Therefore, the common factors of 63 and 64 is 1.

Example 3:

Find the common factors of 63 and 61.

Solution:

The factors of 63 are 1, 3, 7, 9, 21 and 63

The factors of 61 are 1 and 61.

Hence, the common factor of 63 and 61 is 1 only, as 61 is a prime number.

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## Frequently Asked Questions on Factors of 63

### What are the factors of 63?

The factors of 63 are the numbers that divide 63, without leaving any remainder. Hence, the factors of 63 are 1, 3, 7, 9, 21 and 63.

### What is the prime factorization of 63?

The prime factorization of 63 is 3 × 3 × 7 or 32 × 7.

### Write down the positive pair factors of 63?

The positive pair factors of 63 are (1, 63), (3, 21), and (7, 9).

### What are the negative pair factors of 63?

The negative pair factors of 63 are (-1, -63), (-3, -21) and (-7, -9).

### Is 21 a factor of 63?

Yes, 21 is a factor of 63. As the number 21 divides 63 exactly, 21 is a factor of 63.

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