The H.C.F. of 84, 120, and 138 using the prime factorization method is ____.

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Detailed Solution

The H.C.F. of 84, 120, and 138 using the prime factorization method is 6.
We have been given the numbers 84, 120, and 138.
Prime factors of 84, 120 and 138,

84 = 2 × 2 × 3 × 7

120 = 2 × 2 × 2 × 3 × 5

138 = 2 × 3 × 23

Common factors in 84, 120 and 138 are 2 and 3.
The HCF of 84, 120 and 138,

2 × 3 = 6

Therefore, the HCF of 84, 120, and 138 is 6.

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