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).

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Factors of 63: 1, 3, 7, 9, 21 and 63Negative Factors of 63: -1, -3, -7, -9, -21 and -63Prime Factors of 63: 3, 7Prime Factorization of 63: 3 × 3 × 7 = 32 × 7Sum of Factors of 63: 104
1.What are Factors of 63?
2.How to Calculate Factors of 63?
3.Factors of 63 by Prime Factorization
4.Factors of 63 in Pairs
4.Important Notes
4.FAQs on Factors of 63

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 = 63The 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 = 213 × 21 = 63

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Proceeding similarly, we get:

1 × 63 = 633 × 21 = 637 × 9 = 63

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

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:

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It can also be presented as a factor tree:

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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:

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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.
Example 1: Edwin has 63 units of cup sets. He wants to pack it in boxes such that all the units are evenly distributed. There are two sizes of boxes for packing available with him. The first size has a capacity of 14 units and the second size has a capacity of 7 units. Which type of box will he choose so that there is no unit left and maximum units are filled in the boxes? How many units will be stored in each of the boxes?

Solution:

The condition that there is no unit left means when 63 is divided by one of those two numbers i.e. 7 or 14, the remainder must be 0.

That means the number must be a factor of 63.

Out of the two given numbers, 7 is a factor of 63.

Thus, he will choose boxes of the second size of capacity 7 units.

To find the number of units in each box of the second size, we need to divide 63 by 7 i.e. 63/7=9

Hence, the answers are,

Second size

9 units in each box


Example 2: A rectangle has an area of 63 square inches and a length of 21 inches. What will be its breadth?

Solution:

Area of a rectangle = l × b therefore 63 = 21 × ?

We know, 63 = 21× 3. Thus, the breadth is 3.


Example 3: Find the product of all the prime factors of 63.

Solution:

Since, the prime factors of 63 are 3, 7. Therefore, the product of prime factors = 3 × 7 = 21.


Challenging Questions:

Ms. Susan is arranging a field trip for her students to the science park. There are 63 students in all. She plans to divide them into groups such that they are evenly distributed. What are the different combinations she can consider so that the groups are neither too small nor too large?


 

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FAQs on Factors of 63

What are the Factors of 63?

The factors of 63 are 1, 3, 7, 9, 21, 63 and its negative factors are -1, -3, -7, -9, -21, -63.

What is the Greatest Common Factor of 63 and 58?

The factors of 63 are 1, 3, 7, 9, 21, 63 and the factors of 58 are 1, 2, 29, 58. 63 and 58 have only one common factor which is 1. This implies that 63 and 58 are co-prime.Hence, the Greatest Common Factor (GCF) of 63 and 58 is 1.

What are the Prime Factors of 63?

The prime factors of 63 are 3, 7.

What is the Sum of the Factors of 63?

Since all factors of 63 are 1, 3, 7, 9, 21, 63 therefore, the sum of its factors is 1 + 3 + 7 + 9 + 21 + 63 = 104.

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What are the Common Factors of 63 and 32?

Since, the factors of 63 are 1, 3, 7, 9, 21, 63 and factors of 32 are 1, 2, 4, 8, 16, 32. Hence, 63 and 32 have only one common factor which is 1. Therefore, 63 and 32 are co-prime.