Question

$\huge \fbox \mathbb \color{red} \: QUESTION \: : \: \:$

✓ Given that (k - 7) is the H.C.F. of 56 and 104, find the value of k.

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Answer 1

Answer:

the value of k = 15

Step-by-step explanation:

56 = 2³ × 7

104 = 2³ × 13

H.C.F ( 56, 104 ) = 2³ = 8

also,

(k - 7) = 8

=> k = 8 + 7

=> k = 15

Answer 2

Step-by-step explanation:

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HCF = 56 and 104

Find the prime factorization of 56

56 = 2 × 2 × 2 × 7

Find the prime factorization of 104

104 = 2 × 2 × 2 × 13

To find the HCF, multiply all the prime factors common to both numbers:

Therefore, HCF = 2 × 2 × 2

HCF = 8

k-7 = 8

k = 8+7 = 15

k=15