What is the HCF of 21 and 28?

To find the HCF (highest common factor) of two numbers, we need to determine the largest number that divides both of them. One way to do this is to factorize the two numbers into their prime factors and then find the common factors.

To factorize 21, we can observe that it is divisible by 3: 21 ÷ 3 = 7. Thus, 21 = 3 × 7.

To factorize 28, we can observe that it is divisible by 2: 28 ÷ 2 = 14. And 14 is also divisible by 2: 14 ÷ 2 = 7. Thus, 28 = 2 × 2 × 7.

The common factor between 21 and 28 is 7, since they both have 7 as a factor. However, this is not the highest common factor, because 28 is divisible by 2 × 2 = 4, which is also a factor of 21. Therefore, the HCF of 21 and 28 is 7.

Alternatively, we can use the Euclidean algorithm to find the HCF. Starting with the two numbers, we can repeatedly subtract the smaller number from the larger number until one of them becomes zero. The other number will be the HCF.

To apply this algorithm to 21 and 28, we can do:

28 − 21 = 7 21 − 7 = 14 14 − 7 = 7 7 − 7 = 0

Thus, the HCF of 21 and 28 is 7.