Question

find the HCF of the following numbers by prime factorisation method ​

Answer 1

Answer:

1》The HCF of 21 and 105 is 21.

2》The HCF of 14 and 19 is 1.

3》The HCF of 54 and 72 is 18

4》The HCF of 50 and 25 is 25

5》The HCF of 85 and 102 is 17

6》The HCF of 22 and 44 is 22

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Step-by-step explanation:

1》The GCF of 21 and 105 is 21.

Steps to find HCF

Find the prime factorization of 21

21 = 3 × 7

Find the prime factorization of 105

105 = 3 × 5 × 7

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

Therefore, HCF = 3 × 7

HCF = 21

2》Steps to find HCF

Find the prime factorization of 14

14 = 2 × 7

Find the prime factorization of 19

19 = 19

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

Therefore, HCF = 1

3》HCF of 54 and 72 is the largest possible number that divides 54 and 72 exactly without any remainder. The factors of 54 and 72 are 1, 2, 3, 6, 9, 18, 27, 54 and 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 respectively. There are 3 commonly used methods to find the HCF of 54 and 72 - Euclidean algorithm, prime factorization, and long division.

Answer: HCF of 54 and 72 is 18.

4》HCF of 25 and 50 by Listing Common Factors

Therefore, the greatest common factor of 25 and 50 is 25

5》We found the factors and prime factorization of 85 and 102. The biggest common factor number is the GCF number.

So the greatest common factor 85 and 102 is 17.

6》There are 4 common factors of 22 and 44, that are 1, 2, 11, and 22. Therefore, the greatest common factor of 22 and 44 is 22.