GCF of 1, 4 and 9 = 1 (Coprime)
Quick Answer
GCF(1, 4 and 9) = 1. 1, 4 and 9 are coprime (share only the divisor 1).
Common divisors: 1.
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Step-by-Step: Euclidean Algorithm
The Euclidean algorithm finds the GCF by repeated division: divide the larger by the smaller, replace with the remainder, repeat until the remainder is 0. The last non-zero divisor is the GCF.
For 3 numbers, apply Euclidean pairwise: GCF(1, 4, 9) = GCF(GCF(1, 4), 9).
The table below shows the first reduction (between 1 and 4):
| Step | Dividend ÷ Divisor | Quotient | Remainder |
|---|---|---|---|
| 1 | 4 ÷ 1 | 4 | 0 |
GCF(1, 4 and 9) = 1
Common Divisors of 1, 4 and 9
Since 1, 4 and 9 are coprime, the only common divisor is 1.
1, 4 and 9 Are Coprime
Two (or more) integers are coprime (also called relatively prime) when their GCF equals 1 — they share no common divisors other than 1. 1, 4 and 9 qualify.
Note: coprime numbers do not need to be prime individually. For example, 8 and 15 are coprime (GCF = 1), but neither is prime — 8 = 2³ and 15 = 3 × 5 share no prime factors.
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How to Find the Greatest Common Factor
The Greatest Common Factor (GCF) of two or more numbers is the largest positive integer that divides each of the numbers without leaving a remainder.
Method 1: Euclidean Algorithm (used above)
- Divide the larger number by the smaller. Note the remainder.
- Replace the pair (larger, smaller) with (smaller, remainder).
- Repeat until the remainder is 0. The last non-zero divisor is the GCF.
Method 2: Listing Factors
- List all factors of each number
- Identify the factors that appear in all lists (common factors)
- Select the largest common factor — this is the GCF
Method 3: Prime Factorization
- Find the prime factorization of each number
- Identify which prime factors appear in all factorizations
- For each common prime factor, take the lowest exponent
- Multiply these prime factors raised to their lowest exponents
GCF = product of (common prime factors)lowest exponent
Example: GCF(12, 18) using prime factorization
- 12 = 2² × 3¹
- 18 = 2¹ × 3²
- Common primes: 2 and 3 — take the lowest exponent of each
- GCF = 2¹ × 3¹ = 6
Frequently Asked Questions
What is the GCF of 1, 4 and 9?
GCF(1, 4 and 9) = 1. This is the largest integer that divides each of the inputs without remainder.
How do you find the GCF of 1, 4 and 9?
Apply the Euclidean algorithm (see the step-by-step table above). For 3 numbers, reduce pairwise: GCF(a, b, c) = GCF(GCF(a, b), c).
Are 1, 4 and 9 coprime?
Yes. 1, 4 and 9 are coprime (relatively prime) because their GCF is 1 — they share no common divisor other than 1.
What are coprime numbers?
Two or more numbers are coprime (or relatively prime) if their GCF is 1. Example: GCF(8, 15) = 1.
What are other names for GCF?
The GCF is also known as GCD (Greatest Common Divisor, math) and HCF (Highest Common Factor, British education). All three terms are equivalent.
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