GCF of 24 and 33
The GCF of 24 and 33 is 3. 24 ÷ 3 = 8, 33 ÷ 3 = 11.
Method 1: list the factors
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 33: 1, 3, 11, 33
Common factors: 1, 3. The greatest is 3.
Method 2: prime factorisation
24 = 23 × 3
33 = 3 × 11
Take every prime that appears in all of them, with its lowest power: 3 = 3.
Method 3: the division method (Euclid's algorithm)
| Divide | by | Quotient | Remainder |
|---|---|---|---|
| 33 | 24 | 1 | 9 |
| 24 | 9 | 2 | 6 |
| 9 | 6 | 1 | 3 |
| 6 | 3 | 2 | 0 |
The last divisor before the remainder reaches 0 is the GCF: 3. This is the fastest method for large numbers.
GCF × LCM = the product
3 × 264 = 792 and 24 × 33 = 792. For two numbers the GCF times the LCM always equals the product, so the LCM of 24 and 33 is 264.
🧮 Calculator
The answer appears here, with the working in words.
✏️ Five questions, answers hidden
1. Find the GCF of 25 and 33.
Answer: 1
2. Find the GCF of 48 and 66.
Answer: 6
3. Are 24 and 34 co-prime?
Answer: no
4. Find the LCM of 24 and 33.
Answer: 264
5. Simplify the fraction 24/33.
Answer: 8/11
📚 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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