GCF of 3 and 7
The GCF of 3 and 7 is 1. The numbers are co-prime: they share no factor but 1.
Method 1: list the factors
Factors of 3: 1, 3
Factors of 7: 1, 7
Common factors: 1. The greatest is 1.
Method 2: prime factorisation
3 = 3
7 = 7
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 |
|---|---|---|---|
| 7 | 3 | 2 | 1 |
| 3 | 1 | 3 | 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 × 21 = 21 and 3 × 7 = 21. For two numbers the GCF times the LCM always equals the product, so the LCM of 3 and 7 is 21.
🧮 Calculator
The answer appears here, with the working in words.
✏️ Five questions, answers hidden
1. Find the GCF of 4 and 7.
Answer: 1
2. Find the GCF of 6 and 14.
Answer: 2
3. Are 3 and 8 co-prime?
Answer: yes
4. Find the LCM of 3 and 7.
Answer: 21
5. Simplify the fraction 3/7.
Answer: 3/7
📚 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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