Question

Find the highest common factor (HCF) of 308 and 66

Answer 1

The highest common factor (HCF) of 308 and 66 is found using the Euclidean algorithm, resulting in an HCF of 22.

Step-by-step explanation:

To find the highest common factor (HCF) of 308 and 66, we can use the Euclidean algorithm, which involves a series of divisions.

1. First, divide the larger number by the smaller number and find the remainder: 308 ÷ 66 = 4 remainder 44.
2. Then, divide the smaller number (66) by the remainder (44): 66 ÷ 44 = 1 remainder 22.
3. Repeat the process by dividing the last divisor (44) by the last remainder (22): 44 ÷ 22 = 2 with no remainder.
4. When the remainder is 0, the last non-zero remainder is the HCF. So in this case, the HCF of 308 and 66 is 22.

To find the highest common factor (HCF) of 308 and 66, we can start by listing the factors of each number. The factors of 308 are 1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, and 308. The factors of 66 are 1, 2, 3, 6, 11, 22, 33, and 66.

The common factors of 308 and 66 are 1, 2, 11, and 22. The highest common factor (HCF) is the largest of these common factors, which in this case is 22.