Sum of 2 numbers is 128 and their HCF is 8. How many numbers of pairs of numbers will satisfy this condition?

To find the number of pairs of numbers that satisfy the condition, we need to follow these steps:

1. Since the sum of the two numbers is 128 and their highest common factor (HCF) is 8, we can say that the sum of the two numbers when divided by their HCF is 128/8 = 16.

2. Now, we need to find the pairs of numbers that add up to 16 because these pairs, when multiplied by the HCF, will give us the pairs that add up to 128.

3. The pairs of numbers that add up to 16 are (1,15), (2,14), (3,13), (4,12), (5,11), (6,10), (7,9), and (8,8).

4. However, not all of these pairs will satisfy the condition that their HCF is 8.

5. The pairs that have 8 as their HCF are (1,15) and (2,14) because 8 is a factor of both numbers in each pair.

6. Therefore, there are 2 pairs of numbers that satisfy the condition that their sum is 128 and their HCF is 8.