Two numbers are co-prime (also called relatively prime or mutually prime) if their Highest Common Factor (HCF) is 1. They share no common factor other than 1. Examples: (8, 15) are co-prime since HCF(8, 15) = 1. Co-prime numbers need not be prime numbers individually.
Co-prime numbers have HCF = 1.
Examples: (8,15), (4,9), (14,25), (1,n), any consecutive integers.
LCM of co-prime numbers = their product (since HCF=1).
Co-prime numbers need not be individually prime.
Any two consecutive integers are always co-prime.
Two distinct prime numbers are always co-prime.
Two numbers a and b are co-prime if: HCF(a, b) = 1 (They have no common factor other than 1.)
Examples of co-prime pairs: • (8, 15): factors of 8 = {1,2,4,8}; factors of 15 = {1,3,5,15}; HCF = 1 ✓ • (4, 9): factors of 4 = {1,2,4}; factors of 9 = {1,3,9}; HCF = 1 ✓ • (14, 25): factors of 14 = {1,2,7,14}; factors of 25 = {1,5,25}; HCF = 1 ✓ • (1, n): 1 is co-prime with every positive integer • (consecutive integers): any two consecutive integers are always co-prime e.g., (7, 8), (15, 16), (100, 101)
Not co-prime (HCF ≠ 1): • (6, 9): HCF = 3 (both divisible by 3) • (12, 18): HCF = 6
HCF of co-prime numbers = 1.
LCM of co-prime numbers = their product. HCF × LCM = a × b If HCF = 1, then LCM = a × b. Example: LCM(8, 15) = 8 × 15 = 120.
Co-prime numbers need not be prime. (8, 15): neither 8 nor 15 is prime, yet they are co-prime.
Any two consecutive natural numbers are co-prime. (n, n+1) always have HCF = 1.
Two prime numbers are always co-prime to each other. (5, 7): HCF = 1; (11, 13): HCF = 1.
1 is co-prime with every natural number.
Co-prime pairs can share composite numbers. (16, 25): 16 = 2⁴, 25 = 5² — no common prime factor, HCF = 1.
Prime number: a number that has exactly two factors — 1 and itself. Examples: 2, 3, 5, 7, 11, 13...
Co-prime numbers: a pair of numbers whose HCF = 1. Neither number needs to be prime.
Comparison: • Prime: property of a single number • Co-prime: relationship between two (or more) numbers
Examples clarifying the distinction: • (4, 9) — both composite, yet co-prime (HCF=1) • (2, 4) — 2 is prime, 4 is not prime, but NOT co-prime (HCF=2) • (3, 5) — both prime → always co-prime
Test for co-primality: Find HCF. If HCF = 1 → co-prime. If HCF > 1 → not co-prime.
Co-prime numbers (relatively prime) are two numbers whose HCF is 1. They share no common factor other than 1. Examples: (8, 15) and (4, 9) are co-prime pairs.
Yes. Factors of 8: 1,2,4,8. Factors of 15: 1,3,5,15. Common factor = 1 only. So HCF(8,15)=1, and they are co-prime.
LCM of two co-prime numbers = their product. Since HCF=1 and HCF×LCM = a×b, LCM = a×b. Example: LCM(8,15) = 120.
Yes. Any two consecutive integers (n, n+1) always have HCF = 1, so they are always co-prime.
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