Answer :
Final answer:
Using the prime factorization method, the H.C.F of given number pairs such as 24 and 36; 56 and 72; 21 and 35; 45 and 81; and 42 and 49 are calculated as 12, 8, 7, 9, and 7 respectively.
Explanation:
The prime factorization method is used to find the highest common factor (H.C.F) of two numbers by breaking them down into their prime factors and then identifying the common factors among them. Here are the solutions using this method:
24 and 36: Prime factors of 24 are 2³ × 3, and prime factors of 36 are 2² × 3². The H.C.F is 2² × 3 = 12.
56 and 72: Prime factors of 56 are 2³ × 7, and prime factors of 72 are 2³ × 3². The H.C.F is 2³ = 8.21 and 35: Prime factors of 21 are 3 × 7, and prime factors of 35 are 5 × 7. The H.C.F is 7.45 and 81: Prime factors of 45 are 3² × 5, and prime factors of 81 are 3´. The H.C.F is 3² = 9.42 and 49: Prime factors of 42 are 2 × 3 × 7, and prime factors of 49 are 7². The H.C.F is 7.All methods ultimately lead to the same answer, providing a lesson that mathematics offers multiple avenues to reach the same result.
