The GCF of 8 and 100 is 4. The LCM of 8 and 100 is 200.
Factors of 8: 1, 2, 4, 8.
Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100.
Common factors: 1, 2 and 4. The greatest of these is 4.
8 = 2 × 2 × 2
100 = 2 × 2 × 5 × 5
GCF: multiply the prime factors both numbers share: 2 × 2 = 4.
LCM: multiply every prime the maximum number of times it appears in either number: 2 × 2 × 2 × 5 × 5 = 200.
Divide the larger number by the smaller and repeat with the remainder until it is 0. The last non-zero remainder is the GCF.
The last non-zero remainder is 4, so GCF(8, 100) = 4.
Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, ...
Multiples of 100: 100, 200, 300, ...
The first number in both lists is 200.
4 × 200 = 800 = 8 × 100. This always holds for two numbers, so you can find the LCM as (8 × 100) ÷ 4 = 200.
Divide the top and bottom by the GCF 4: 8/100 = 2/25.
| Numbers | GCF | LCM |
|---|---|---|
| 2 and 8 | 2 | 8 |
| 3 and 8 | 1 | 24 |
| 4 and 8 | 4 | 8 |
| 5 and 8 | 1 | 40 |
| 6 and 8 | 2 | 24 |
| 7 and 8 | 1 | 56 |
| 2 and 100 | 2 | 100 |
| 3 and 100 | 1 | 300 |
| 4 and 100 | 4 | 100 |
| 5 and 100 | 5 | 100 |
| 6 and 100 | 2 | 300 |
| 7 and 100 | 1 | 700 |
See also: factors of 8 · factors of 100.
Different numbers? Use the GCF and LCM calculator (any amount of numbers) or browse all GCF and LCM pairs.