What is HCF of 14 and 21?

Answer 1

The GCF is 7.

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The prime factorisation method:

14 = 2 × 7

21 = 3 × 7

hcf = 7 as it is the only common prime between the two factorisations.

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Euclid's method:

1. find the remainder of the first number divided by the second number
2. replace the first number by the second number
3. replace the second number by the remainder
4. if the second number/remainder is not zero repeat from step 1
5. hcf = first number

For 14 and 21 this gives:

1) 14 ÷ 21 → remainder 14

2) first number becomes 21

3) second number becomes 14

4) 14 is not 0, so repeat form step 1

1) 21 ÷ 14 → remainder 7

2) first number becomes 14

3) second number becomes 7

4) 7 is not 0, so repeat form step 1

1) 14 ÷ 7 → remainder 0

2) first number becomes 7

3) second number becomes 0

4) 0 is 0, so continue to step 5

5) hcf is first number which is now 7

→ hcf(14, 21) = 7.