HCF of 100 and 190
The HCF of 100 and 190 is 10. 100 ÷ 10 = 10, 190 ÷ 10 = 19.
Method 1: list the factors
Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
Factors of 190: 1, 2, 5, 10, 19, 38, 95, 190
Common factors: 1, 2, 5, 10. The greatest is 10.
Method 2: prime factorisation
100 = 22 × 52
190 = 2 × 5 × 19
Take every prime that appears in all of them, with its lowest power: 2 × 5 = 10.
Method 3: the division method (Euclid's algorithm)
| Divide | by | Quotient | Remainder |
|---|---|---|---|
| 190 | 100 | 1 | 90 |
| 100 | 90 | 1 | 10 |
| 90 | 10 | 9 | 0 |
The last divisor before the remainder reaches 0 is the HCF: 10. This is the fastest method for large numbers.
HCF × LCM = the product
10 × 1,900 = 19,000 and 100 × 190 = 19,000. For two numbers the HCF times the LCM always equals the product, so the LCM of 100 and 190 is 1,900.
🧮 Calculator
The answer appears here, with the working in words.
✏️ Five questions, answers hidden
1. Find the HCF of 101 and 190.
Answer: 1
2. Find the HCF of 200 and 380.
Answer: 20
3. Are 100 and 191 co-prime?
Answer: yes
4. Find the LCM of 100 and 190.
Answer: 1,900
5. Simplify the fraction 100/190.
Answer: 10/19
📚 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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