To test whether the given pairs of numbers are coprime, we need to check if the greatest common divisor (GCD) of each pair is 1. Two numbers are considered coprime if their GCD is 1, meaning they have no common factors other than 1.
Let's address each pair:
### Pair (16, 21)
1. Factors of 16: 1, 2, 4, 8, 16
2. Factors of 21: 1, 3, 7, 21
The common factor between 16 and 21 is only 1. Hence, 16 and 21 are coprime.
### Pair (24, 48)
1. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
2. Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
The common factors between 24 and 48 are 1, 2, 3, 4, 6, 8, 12, and 24, which means they have common factors other than 1. Thus, 24 and 48 are not coprime.
### Pair (10, 100)
1. Factors of 10: 1, 2, 5, 10
2. Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
The common factors between 10 and 100 are 1, 2, 5, and 10, again indicating that they have common factors other than 1. Hence, 10 and 100 are not coprime.
### Summary
- 16 and 21 are coprime.
- 24 and 48 are not coprime.
- 10 and 100 are not coprime.
