Factor of 63 Using Prime Factorization
Factors of 63
The integers that divide 63 exactly are called factors of 63. 63 has more than two factors since it is a composite number. Factors of 63 cannot be in a fraction or decimal form. There are six factors for 63, which are 1, 3, 7, 9, 21, and 63. As a result, the lowest factor is 1 and the largest factor of 63 is 63.
Factor Pairs of 63
The numbers that result in 63 when multiplied in pairs are known as the factor pairs of 63. (1, 63), (3, 21) and (7, 9) are the factor pairs of 63. When all the factors of 63 are added together, the result is 1 + 3 + 7 + 9 + 21 + 63 = 104.
Deriving the Factor List of 63
Here is a list of the numbers which are factors of 63.
Factor tree of 63 is given below:
Prime factorization of 63 is the method of expressing 63 as a product of its prime factors.
Hence, the prime factorization of 63 can be written as: \(3~\times~3~\times~7~=~3^2~\times~7\)
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Solved Factors of 63 Examples
Example 1:
Write a list of the common factors of 63 and 62.
Solution:
The factors of 63 = 1, 3, 7, 9, 21 and 63
The factors of 62 = 1, 2, 31, 62.
The only 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 factor of 63 and 64 is 1.
Example 3:
Is the number 21 a factor of 63?
Solution:
Yes, 21 is a factor of 63 because it divides 63 exactly, that is leaving no remainder.
Example 4:
Three people completed 63 tasks in 21 days. Is there a better way to complete the same set of tasks within a shorter period if the number of people can be increased? Note that the tasks are always divided equally among the workers.
Solution:
The factor pairs of 63 are (1, 63), (3, 21) and (7, 9). To complete the same number of tasks in a shorter period, we need to increase the number of workers.
(3, 21) implies that either 3 workers can complete the tasks in 21 days or 21 workers can complete the tasks in 3 days.
So, the best way to complete the 63 tasks in the shortest time period is to hire 63 workers, so that the tasks will be completed in a day.
The numbers that divide 63 without leaving any remainder are known as factors of 63. As a result, the factors of 63 are 1, 3, 7, 9, 21, and 63.
\(3~\times~3~\times~7\) or \(3^2~\times~7\) is the prime factorization of 63.
(1, 63), (3, 21), and (7, 9) are the positive pair factors of 63.