Co-Prime Numbers List & Rules (1 to 100)
Co-prime numbers are two numbers whose highest common factor (HCF) is 1, like 14 and 15. Among the numbers 1 to 100 there are exactly 3,043 distinct co-prime pairs. Consecutive numbers and any two different primes are always co-prime.
Core ConditionHCF (GCD) = 1highest common factor
Prime PairsAlways Co-Primetwo different primes
Consecutive PairAlways Co-Primen and n + 1
Pair of 1Always Co-Prime with N1 and any number N
Two-Number Co-Prime Checker
HCF(14, 15) = 1, so Yes, Co-Prime!
Euclid steps: 15 = 1 x 14 + 1, then 14 = 14 x 1 + 0
Why: consecutive numbers are always co-prime.
4 Foundational Rules of Co-Prime Numbers
| Rule | What It Means | Example |
|---|---|---|
| Rule 1: HCF must be 1 | Two numbers are co-prime (also called relatively prime) when their highest common factor is 1. The numbers themselves do not have to be prime. | 8 and 9 are co-prime: HCF = 1, but neither is prime. |
| Rule 2: Two different primes | Any two different prime numbers are co-prime. A prime and another number are co-prime unless the prime divides that number. | 7 and 13 are co-prime. 5 and 20 are not (HCF = 5). |
| Rule 3: Consecutive numbers | n and n + 1 are always co-prime. Consecutive odd numbers (n and n + 2, with n odd) are co-prime too, but two consecutive even numbers never are. | 99 and 100 are co-prime. 25 and 27 are co-prime. |
| Rule 4: 1 and even numbers | 1 is co-prime with every number, since its only factor is 1. Two even numbers are never co-prime, because both are divisible by 2. | 1 and 50 are co-prime. 12 and 18 are not (HCF = 6). |
| Pair (A, B) | Prime Factors | HCF (GCD) | Why Co-Prime | Test |
|---|---|---|---|---|
| Numbers 1 to 20: 15 of 127 co-prime pairs shown | ||||
| (1, 20) | 1 = none 20 = 2² × 5 | 1 | Includes 1 | |
| (7, 8) | 7 = 7 8 = 2³ | 1 | Consecutive numbers | |
| (14, 15) | 14 = 2 × 7 15 = 3 × 5 | 1 | Consecutive numbers | |
| (19, 20) | 19 = 19 20 = 2² × 5 | 1 | Consecutive numbers | |
| (2, 13) | 2 = 2 13 = 13 | 1 | Two different primes | |
| (5, 17) | 5 = 5 17 = 17 | 1 | Two different primes | |
| (7, 19) | 7 = 7 19 = 19 | 1 | Two different primes | |
| (9, 11) | 9 = 3² 11 = 11 | 1 | Consecutive odd numbers | |
| (13, 15) | 13 = 13 15 = 3 × 5 | 1 | Consecutive odd numbers | |
| (3, 10) | 3 = 3 10 = 2 × 5 | 1 | Prime and composite | |
| (5, 12) | 5 = 5 12 = 2² × 3 | 1 | Prime and composite | |
| (7, 18) | 7 = 7 18 = 2 × 3² | 1 | Prime and composite | |
| (4, 9) | 4 = 2² 9 = 3² | 1 | Composite and composite | |
| (8, 15) | 8 = 2³ 15 = 3 × 5 | 1 | Composite and composite | |
| (9, 14) | 9 = 3² 14 = 2 × 7 | 1 | Composite and composite | |
| Numbers 21 to 50: 15 of 272 co-prime pairs shown | ||||
| (21, 22) | 21 = 3 × 7 22 = 2 × 11 | 1 | Consecutive numbers | |
| (34, 35) | 34 = 2 × 17 35 = 5 × 7 | 1 | Consecutive numbers | |
| (49, 50) | 49 = 7² 50 = 2 × 5² | 1 | Consecutive numbers | |
| (23, 31) | 23 = 23 31 = 31 | 1 | Two different primes | |
| (29, 47) | 29 = 29 47 = 47 | 1 | Two different primes | |
| (37, 41) | 37 = 37 41 = 41 | 1 | Two different primes | |
| (25, 27) | 25 = 5² 27 = 3³ | 1 | Consecutive odd numbers | |
| (33, 35) | 33 = 3 × 11 35 = 5 × 7 | 1 | Consecutive odd numbers | |
| (45, 47) | 45 = 3² × 5 47 = 47 | 1 | Consecutive odd numbers | |
| (23, 40) | 23 = 23 40 = 2³ × 5 | 1 | Prime and composite | |
| (31, 48) | 31 = 31 48 = 2⁴ × 3 | 1 | Prime and composite | |
| (37, 50) | 37 = 37 50 = 2 × 5² | 1 | Prime and composite | |
| (21, 32) | 21 = 3 × 7 32 = 2⁵ | 1 | Composite and composite | |
| (25, 36) | 25 = 5² 36 = 2² × 3² | 1 | Composite and composite | |
| (35, 48) | 35 = 5 × 7 48 = 2⁴ × 3 | 1 | Composite and composite | |
| Numbers 51 to 100: 15 of 748 co-prime pairs shown | ||||
| (51, 52) | 51 = 3 × 17 52 = 2² × 13 | 1 | Consecutive numbers | |
| (77, 78) | 77 = 7 × 11 78 = 2 × 3 × 13 | 1 | Consecutive numbers | |
| (99, 100) | 99 = 3² × 11 100 = 2² × 5² | 1 | Consecutive numbers | |
| (53, 59) | 53 = 53 59 = 59 | 1 | Two different primes | |
| (61, 97) | 61 = 61 97 = 97 | 1 | Two different primes | |
| (71, 89) | 71 = 71 89 = 89 | 1 | Two different primes | |
| (55, 57) | 55 = 5 × 11 57 = 3 × 19 | 1 | Consecutive odd numbers | |
| (75, 77) | 75 = 3 × 5² 77 = 7 × 11 | 1 | Consecutive odd numbers | |
| (91, 93) | 91 = 7 × 13 93 = 3 × 31 | 1 | Consecutive odd numbers | |
| (53, 90) | 53 = 53 90 = 2 × 3² × 5 | 1 | Prime and composite | |
| (67, 100) | 67 = 67 100 = 2² × 5² | 1 | Prime and composite | |
| (73, 96) | 73 = 73 96 = 2⁵ × 3 | 1 | Prime and composite | |
| (51, 70) | 51 = 3 × 17 70 = 2 × 5 × 7 | 1 | Composite and composite | |
| (64, 81) | 64 = 2⁶ 81 = 3⁴ | 1 | Composite and composite | |
| (85, 96) | 85 = 5 × 17 96 = 2⁵ × 3 | 1 | Composite and composite | |
Pairs are counted as (A, B) with A < B, with both numbers inside the interval. Press Test to load a pair into the checker above.
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Frequently Asked Questions
| Question | Answer |
|---|---|
| What are co-prime numbers? | Co-prime numbers, also called relatively prime numbers, are two numbers whose highest common factor (HCF or GCD) is 1, such as 14 and 15. |
| How do you check if two numbers are co-prime? | Find the HCF of the two numbers using prime factors or the Euclidean algorithm. If the HCF is 1, the numbers are co-prime; for 14 and 15 the HCF is 1. |
| Do co-prime numbers have to be prime? | No. Neither number has to be prime, for example 8 and 9 are co-prime because their HCF is 1. |
| Are two prime numbers always co-prime? | Any two different prime numbers are co-prime, such as 7 and 13. The same prime twice, such as 7 and 7, has an HCF of 7, so it is not co-prime. |
| Are consecutive numbers always co-prime? | Yes. Any two consecutive numbers n and n + 1 have an HCF of 1, for example 99 and 100. |
| Can two even numbers be co-prime? | No. Two even numbers are both divisible by 2, so their HCF is at least 2, for example 12 and 18 have an HCF of 6. |
Related Number Theory References
| Related Page | What You Will Find |
|---|---|
| Prime Numbers (1-1000) | All 168 primes up to 1000 with a prime checker and distribution table. |
| Twin Primes up to 1000 | All 35 twin prime pairs with an instant pair checker. |
| Prime Factorization Table (1-100) | Prime factors and exponential form for every number from 1 to 100. |