What is HCF of 56,40,96
Answers
Answer:
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Answer:
Prime factorization of 56, 96 and 404 is given as,
56 = 2 × 2 × 2 × 7
96 = 2 × 2 × 2 × 2 × 2 × 3
404 = 2 × 2 × 101
LCM(56, 96) = 672, LCM(96, 404) = 9696, LCM(404, 56) = 5656, LCM(56, 96, 404) = 67872
⇒ HCF(56, 96, 404) = [(56 × 96 × 404) × LCM(56, 96, 404)]/[LCM(56, 96) × LCM (96, 404) × LCM(404, 56)]
⇒ HCF(56, 96, 404) = (2171904 × 67872)/(672 × 9696 × 5656)
⇒ HCF(56, 96, 404) = 4.
Therefore, the HCF of 56, 96 and 404 is 4.
Example 2: Verify the relation between the LCM and HCF of 56, 96 and 404.
Solution:
The relation between the LCM and HCF of 56, 96 and 404 is given as, HCF(56, 96, 404) = [(56 × 96 × 404) × LCM(56, 96, 404)]/[LCM(56, 96) × LCM (96, 404) × LCM(56, 404)]
⇒ Prime factorization of 56, 96 and 404:
56 = 2 × 2 × 2 × 7
96 = 2 × 2 × 2 × 2 × 2 × 3
404 = 2 × 2 × 101
∴ LCM of (56, 96), (96, 404), (56, 404), and (56, 96, 404) is 672, 9696, 5656, and 67872 respectively.
Now, LHS = HCF(56, 96, 404) = 4.
And, RHS = [(56 × 96 × 404) × LCM(56, 96, 404)]/[LCM(56, 96) × LCM (96, 404) × LCM(56, 404)] = [(2171904) × 67872]/[672 × 9696 × 5656]
LHS = RHS = 4.
Hence verified.
Example 3: Find the highest number that divides 56, 96, and 404 completely.
Solution:
The highest number that divides 56, 96, and 404 exactly is their highest common factor.
Factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56
Factors of 96 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
Factors of 404 = 1, 2, 4, 101, 202, 404
The HCF of 56, 96, and 404 is 4.
∴ The highest number that divides 56, 96, and 404 is 4.