Factors of 100
What are the Factors of 100?
The factors of 100 are integers that divide 100 without leaving any remainder. In other words, the factors of 100 divide 100 evenly.
Example: 5 is a factor of 100 because when we divide 100 by 5, it gives us 20 as the quotient and 0 as the remainder. Here, the quotient 20 is also a factor of 100.
So, to check if any number is a factor of 100 or not, divide 100 by that number and verify whether the remainder is zero or not.
Factor List of 100
The factors of 100 can be obtained by applying the divisibility rules and division facts.
The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50 and 100.
Prime Factors of 100
A factor tree can be used to learn about the prime factorization of 100.
From the factor tree, we can see that the prime factorization of 100 is 2 × 2 × 5 × 5 = 2\(^2\) × 5\(^2\).
This means that 2 and 5 are the prime factors of 100.
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Factor Pairs of 100
The factor pair of 100 is the combination of two factors of 100 that, when multiplied together, result in 100.
The factors of 100: 1, 2, 4, 5, 10, 20, 25, 50 and 100.
Example: (2, 50) is the factor pair of 100.
The factor pair can be a positive pair or a negative pair.
Positive Factor Pairs of 100
Rapid Recall
Solved Factors of 100 Examples
Example 1: Find the common factors of 55 and 100.
Solution:
The factors of 100: 1, 2, 4, 5, 10, 20, 25, 50 and 100.
The factors of 55: 1, 5 and 11.
So, the common factors of 55 and 100 are 1 and 5.
Example 2: How many factors does 100 have?
Solution:
The factors of 100: 1, 2, 4, 5, 10, 20, 25, 50 and 100.
So, there are 9 factors of 100.
Example 3: Find the product of all the prime factors of 100.
Solution:
The prime factors of 100 are 2 and 5.
The product of the prime factors = 2 × 5
= 10.
So, the product of all the prime factors of 100 is 10.
Example 4: A school library has a collection of 100 books on the history of Europe. The books are to be arranged evenly on 25 shelves. How many books will be placed on each shelf?
Solution:
100 books are to be evenly arranged on 25 shelves.
To find out the number of books that can be placed on each shelf, we will divide 100 by 25, that is,
\(\frac{100}{25}\)
= \(\frac{25~\times~4}{25}\) [(25, 4) is a factor pair of 100]
= 4 [Divide both the numerator and the denominator by 25]
As a result, 4 books can be placed on each shelf.
No, when you divide 100 by 9, it will leave 1 as a remainder, that is, 9 does not divide 100 evenly.
The numbers that divide 100 evenly or leave no remainder behind, are known as the factors of 100.
The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50 and 100.
Hence, the sum of all the factors of 100 is
= 1 + 2 + 4 + 5 + 10 + 20 + 25 + 50 + 100 = 217
Hence, the sum is 217.
Yes, 100 is a composite number as it has factors other than one and itself. It has the factors 1, 2, 4, 5, 10, 20, 25 and 50 other than 1 and 100.
The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50 and 100.
So, the smallest factor of 100 is 1, and the greatest factor is 100 itself.