Factors of 63

Factors of 63 are integers that can be divided evenly into 63. There are overall 6 factors of 63 i.e. 1, 3, 7, 9, 21, and 63 where 63 is the biggest factor. The sum of all factors of 63 is 104 and its factors in Pairs are (1, 63), (3, 21), and (7, 9).

• Factors of 63: 1, 3, 7, 9, 21 and 63
• Negative Factors of 63: -1, -3, -7, -9, -21 and -63
• Prime Factors of 63: 3, 7
• Prime Factorization of 63: 3 × 3 × 7 = 3² × 7
• Sum of Factors of 63: 104

What are Factors of 63?

The number 63 is an odd composite number. As it is odd, it will not have 2 or any multiples of 2 as its factor. To understand why it is composite, let's recall the definition of a composite number. A number is said to be composite if it has more than two factors. Consider the number 11. It has only two factors, which are 1 and 11.

Now, let's consider 60. The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. There are more than two factors of 60. Thus, 60 is a composite number whereas 11 is not.

Similarly, 63 is a composite number as it has more than two factors. Coming back to 63, the factors of 63 are all the integers that 63 can be divided into.

How to Calculate the Factors of 63?

Let's begin calculating the factors of 63 starting with the smallest whole number, i.e. 1.

• Divide 63 with this number. Is the remainder 0? Yes! So, we will get, 63/1 = 63 and 63 × 1 = 63
• The next whole number is 2. Now divide 63 with this number. Is the remainder 0? Definitely no!
• As already discussed in the earlier section, no even number can divide 63.

Hence, we need to check odd numbers only:

• 63/3 = 21
• 3 × 21 = 63

Proceeding similarly, we get:

• 1 × 63 = 63
• 3 × 21 = 63
• 7 × 9 = 63

Hence, the factors of 63 are 1, 3, 7, 9, 21, and 63. Explore factors using illustrations and interactive examples:

• Factors of 36 - The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
• Factors of 70 - The factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70
• Factors of 72 - The factors of 72 are 1, 2, 3, 4, 6, 8, 9 12, 18, 24, 36, 72
• Factors of 48 - The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
• Factors of 81 - The factors of 81 are 1, 3, 9, 27, 81
• Factors of 42 - The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42

Factors of 63 by Prime Factorization

Prime factorization means to express a composite number as the product of its prime factors. To get the prime factorization of 63, we divide it by its smallest prime factor which is 3.

• 63/3 = 21

Now, 21 is divided by its smallest prime factor and the quotient is obtained. This process goes on till we get the quotient as 1. The prime factorization of 63 is shown below:

It can also be presented as a factor tree:

Factors of 63 in Pairs

The pair of numbers that give 63 when multiplied is known as factor pairs of 63. Following are the factors of 63 in pairs:

If we consider negative integers, then both the numbers in the pair factors will be negative. 63 is positive and - ve × - ve = +ve.

Hence, we can have factor pairs of 63 as (-1,-63), (-3,-21), and (-7,-9).

Important Notes:

• As 63 is an odd number, all its factors will also be odd.
• 63 is a non-perfect square number. Thus, it will have an even number of factors. This property holds for every non-perfect square number.