Factor of 84 using Prime Factorization
What are the Factors of 84?
Factors of 84 are the positive numbers that divide the number 84 without leaving any remainder. We will get a remainder if we divide 84 by a number that is not its factor. The factors of 84 are:
To learn more about factors, read the article here.
Prime Factorization of 84
Since 84 is a composite number, we can rewrite the factors to get the prime factorization. Prime factorization of 84 can be represented using a factor tree as follows:
So, the prime factorization of 84 gives us 2 \( \times \) 2 \( \times \) 3 \( \times \) 7.
Factor Pairs of 84
The factors of 84 can be grouped as pairs such that the product of the two factors in the pair is 84. The factor pairs of 84 are:
1 × 84 = 84
2 × 42 = 84
3 × 28 = 84
4 × 21 = 84
6 × 14 = 84
7 × 12 = 84
We can also write the factor pairs in ordered pairs as: (1, 84), (2, 42), (3, 28), (4, 21), (6, 14) and (7, 12).
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Solved Factors of 84 Examples
Example 1: Jan distributed 84 chocolates among 21 friends. How many chocolates did each friend get?
Solution:
Total number of chocolates = 84
Total number of friends = 21
To find the number of chocolates that each friend got, we just need to know the factor pair of 84 which includes 21. The factor pair is (4,21).
Therefore, each friend got 4 chocolates.
Example 2: Find the Greatest Common Factor (GCF) of 84 and 48.
Solution:
The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 and 84.
The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.
So, the greatest common factor or GCF of 84 and 48 is 12.
The number 84 has 12 factors. They are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84.
The factor pairs of 84 are (1, 84), (2, 42), (3, 28), (4, 21), (6, 14) and (7, 12).
The prime factorization of 84 gives us 2 \( \times \) 2 \( \times \) 3 \( \times \) 7.