Answered

Discover a wealth of information and get your questions answered on IDNLearn.com. Our platform is designed to provide reliable and thorough answers to all your questions, no matter the topic.

Test whether the following numbers are co-prime or not.

i) [tex]16, 21[/tex]

ii) [tex]24, 48[/tex]

iii) [tex]10, 100[/tex]

Sagot :

GinnyAnsweridn
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.
Thank you for participating in our discussion. We value every contribution. Keep sharing knowledge and helping others find the answers they need. Let's create a dynamic and informative learning environment together. Your questions find clarity at IDNLearn.com. Thanks for stopping by, and come back for more dependable solutions.