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Use the lists of factors to answer the question:

Factors of [tex]$9$[/tex]: 1, 3, 9
Factors of [tex]$15$[/tex]: 1, 3, 5, 15
Factors of [tex]$21$[/tex]: 1, 3, 7, 21
Factors of [tex]$40$[/tex]: 1, 2, 4, 5, 8, 10, 20, 40

Which pairs of numbers are relatively prime? Check all that apply.

A. 9 and 15
B. 9 and 40
C. 9 and 21
D. 15 and 21
E. 21 and 40

Sagot :

GinnyAnsweridn
To determine which pairs of numbers are relatively prime, we need to identify pairs of numbers that have no common factors other than 1.

Here’s a step-by-step breakdown for each pair of numbers:

1. 9 and 15:
- Factors of 9: {1, 3, 9}
- Factors of 15: {1, 3, 5, 15}
- Common factors: {1, 3}
- Since the common factors include 3, 9 and 15 are not relatively prime.

2. 9 and 40:
- Factors of 9: {1, 3, 9}
- Factors of 40: {1, 2, 4, 5, 8, 10, 20, 40}
- Common factors: {1}
- The only common factor is 1, so 9 and 40 are relatively prime.

3. 9 and 21:
- Factors of 9: {1, 3, 9}
- Factors of 21: {1, 3, 7, 21}
- Common factors: {1, 3}
- Since the common factors include 3, 9 and 21 are not relatively prime.

4. 15 and 21:
- Factors of 15: {1, 3, 5, 15}
- Factors of 21: {1, 3, 7, 21}
- Common factors: {1, 3}
- Since the common factors include 3, 15 and 21 are not relatively prime.

5. 21 and 40:
- Factors of 21: {1, 3, 7, 21}
- Factors of 40: {1, 2, 4, 5, 8, 10, 20, 40}
- Common factors: {1}
- The only common factor is 1, so 21 and 40 are relatively prime.

Therefore, the pairs of numbers that are relatively prime are:
- 9 and 40
- 21 and 40
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