GCF of 2 and 3
The GCF of 2 and 3 is 1. The numbers are co-prime: they share no factor but 1.
Method 1: list the factors
Factors of 2: 1, 2
Factors of 3: 1, 3
Common factors: 1. The greatest is 1.
Method 2: prime factorisation
2 = 2
3 = 3
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 |
|---|---|---|---|
| 3 | 2 | 1 | 1 |
| 2 | 1 | 2 | 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 × 6 = 6 and 2 × 3 = 6. For two numbers the GCF times the LCM always equals the product, so the LCM of 2 and 3 is 6.
🧮 Calculator
The answer appears here, with the working in words.
✏️ Five questions, answers hidden
1. Find the GCF of 3 and 3.
Answer: 3
2. Find the GCF of 4 and 6.
Answer: 2
3. Are 2 and 4 co-prime?
Answer: no
4. Find the LCM of 2 and 3.
Answer: 6
5. Simplify the fraction 2/3.
Answer: 2/3
📚 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.
If this page is the homework and the method is not sticking, that is what a 1-on-1 class fixes: one tutor with a master's degree, one child, on a shared whiteboard, in your time zone, about US$10 to $13 an hour. How 1-on-1 online tutoring works.