GCF of 5 and 9
The GCF of 5 and 9 is 1. The numbers are co-prime: they share no factor but 1.
Method 1: list the factors
Factors of 5: 1, 5
Factors of 9: 1, 3, 9
Common factors: 1. The greatest is 1.
Method 2: prime factorisation
5 = 5
9 = 32
Take every prime that appears in all of them, with its lowest power: 1 = 1.
Method 3: the division method (Euclid's algorithm)
| Divide | by | Quotient | Remainder |
|---|---|---|---|
| 9 | 5 | 1 | 4 |
| 5 | 4 | 1 | 1 |
| 4 | 1 | 4 | 0 |
The last divisor before the remainder reaches 0 is the GCF: 1. This is the fastest method for large numbers.
GCF × LCM = the product
1 × 45 = 45 and 5 × 9 = 45. For two numbers the GCF times the LCM always equals the product, so the LCM of 5 and 9 is 45.
🧮 Calculator
The answer appears here, with the working in words.
✏️ Five questions, answers hidden
1. Find the GCF of 6 and 9.
Answer: 3
2. Find the GCF of 10 and 18.
Answer: 2
3. Are 5 and 10 co-prime?
Answer: no
4. Find the LCM of 5 and 9.
Answer: 45
5. Simplify the fraction 5/9.
Answer: 5/9
📚 The class this belongs to
The greatest common factor is taught in Grade 5 and 6 in the US (Common Core 6.NS.4) and Year 6 in Australia; the same idea is called the HCF in the UK and India.
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