HCF of 399 and 437
The HCF of 399 and 437 is 19. 399 ÷ 19 = 21, 437 ÷ 19 = 23.
Method 1: list the factors
Factors of 399: 1, 3, 7, 19, 21, 57, 133, 399
Factors of 437: 1, 19, 23, 437
Common factors: 1, 19. The greatest is 19.
Method 2: prime factorisation
399 = 3 × 7 × 19
437 = 19 × 23
Take every prime that appears in all of them, with its lowest power: 19 = 19.
Method 3: the division method (Euclid's algorithm)
| Divide | by | Quotient | Remainder |
|---|---|---|---|
| 437 | 399 | 1 | 38 |
| 399 | 38 | 10 | 19 |
| 38 | 19 | 2 | 0 |
The last divisor before the remainder reaches 0 is the HCF: 19. This is the fastest method for large numbers.
HCF × LCM = the product
19 × 9,177 = 174,363 and 399 × 437 = 174,363. For two numbers the HCF times the LCM always equals the product, so the LCM of 399 and 437 is 9,177.
🧮 Calculator
The answer appears here, with the working in words.
✏️ Five questions, answers hidden
1. Find the HCF of 400 and 437.
Answer: 1
2. Find the HCF of 798 and 874.
Answer: 38
3. Are 399 and 438 co-prime?
Answer: no
4. Find the LCM of 399 and 437.
Answer: 9,177
5. Simplify the fraction 399/437.
Answer: 21/23
📚 The class this belongs to
The HCF is taught in Year 6 and 7 in the UK (KS2 and KS3), Class 5 and 6 in CBSE (NCERT Class 6, Playing with Numbers) and Year 6 in Australia; in the US it is the GCF.
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