GCF and LCM of 8 and 25

The GCF of 8 and 25 is 1. The LCM of 8 and 25 is 200.

8 and 25 share no common factor except 1, so they are coprime (relatively prime). When two numbers are coprime their LCM is simply their product: 8 × 25 = 200.

Method 1: list the factors (GCF)

Factors of 8: 1, 2, 4, 8.
Factors of 25: 1, 5, 25.
Common factors: 1. The greatest of these is 1.

Method 2: prime factorization

8 = 2 × 2 × 2
25 = 5 × 5

GCF: multiply the prime factors both numbers share: there are none, so the GCF is 1.

LCM: multiply every prime the maximum number of times it appears in either number: 2 × 2 × 2 × 5 × 5 = 200.

Method 3: Euclidean algorithm (GCF)

Divide the larger number by the smaller and repeat with the remainder until it is 0. The last non-zero remainder is the GCF.

  1. 25 = 3 × 8 + 1
  2. 8 = 8 × 1 + 0

The last non-zero remainder is 1, so GCF(8, 25) = 1.

LCM by listing multiples

Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, ...
Multiples of 25: 25, 50, 75, 100, 125, 150, 175, 200, 225, ...
The first number in both lists is 200.

Check: GCF × LCM = product

1 × 200 = 200 = 8 × 25. This always holds for two numbers, so you can find the LCM as (8 × 25) ÷ 1 = 200.

Simplifying the fraction 8/25

8/25 is already in lowest terms because the GCF of 8 and 25 is 1.

GCF and LCM of similar pairs

NumbersGCFLCM
2 and 828
3 and 8124
4 and 848
5 and 8140
6 and 8224
7 and 8156
2 and 25150
3 and 25175
4 and 251100
5 and 25525
6 and 251150
7 and 251175

See also: factors of 8 · factors of 25 · 8/25 as a decimal.

Different numbers? Use the GCF and LCM calculator (any amount of numbers) or browse all GCF and LCM pairs.