RELATIVELY PRIME NUMBERS

Relatively Prime Numbers

Definition Of Relatively Prime Numbers

Two integers a and b are said to be relatively prime if they do not have any common factor other than 1 or - 1.

More about Relatively Prime Numbers

Relatively prime numbers are also called as co-primes.

Example of Relatively Prime Numbers

12 and 13 are relatively prime numbers as there are no common factors between 12 and 13 other than 1.

Video Examples: What are Relatively Prime Numbers?

Solved Example on Relatively Prime Numbers

Ques: Choose the pair of relatively prime numbers in the following.

Choices:

A. (7, 14)
B. (8, 16)
C. (6, 13)
D. (6, 12)
Correct Answer: C

Solution:

Step 1: Two numbers are said to be relatively prime if their common factor is only 1
Step 2: Common factors of 6 and 12 are 1, 2, 3, 6
Step 3: Common factors of 7 and 14 are 1, 7
Step 4: Common factors of 8 and 16 are 1, 2, 4, 8
Step 5: Common factor of 6 and 13 is only 1
Step 6: (6, 13) is a pair of relatively prime numbers.

Quick Summary

Relatively prime numbers are also called co-primes.
Relatively prime numbers share no common factors other than 1.
The greatest common divisor (GCD) of relatively prime numbers is 1.

\[ gcd(a, b) = 1 \]

🍎 Teacher Insights

Use visual aids like Venn diagrams to illustrate the concept of common factors and how relatively prime numbers have no overlapping sets of factors (other than 1). Provide various examples and non-examples to clarify the definition.

🎓 Prerequisites

Factors
Greatest Common Factor (GCF)
Integers

Check Your Knowledge

Q1: Which of the following pairs of numbers are relatively prime?

(12, 18) (15, 25) (14, 21) (8, 15)

Q2: What is the greatest common divisor (GCD) of two relatively prime numbers?

0 1 2 The product of the numbers

Frequently Asked Questions

Q: Are prime numbers always relatively prime to each other?
A: Yes, distinct prime numbers are always relatively prime to each other because they only have 1 and themselves as factors.

Q: Can two composite numbers be relatively prime?
A: Yes, two composite numbers can be relatively prime if they share no common factors other than 1. For example, 8 and 9 are both composite but are relatively prime.