GCF and LCM of 25 and 40

The GCF of 25 and 40 is 5. The LCM of 25 and 40 is 200.

• GCF (greatest common factor, also called GCD or HCF) of 25 and 40 = 5
• LCM (least common multiple) of 25 and 40 = 200

Method 1: list the factors (GCF)

Factors of 25: 1, 5, 25.
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40.
Common factors: 1 and 5. The greatest of these is 5.

Method 2: prime factorization

25 = 5 × 5
40 = 2 × 2 × 2 × 5

GCF: multiply the prime factors both numbers share: 5 = 5.

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. 40 = 1 × 25 + 15
2. 25 = 1 × 15 + 10
3. 15 = 1 × 10 + 5
4. 10 = 2 × 5 + 0

The last non-zero remainder is 5, so GCF(25, 40) = 5.

LCM by listing multiples

Multiples of 25: 25, 50, 75, 100, 125, 150, 175, 200, 225, ...
Multiples of 40: 40, 80, 120, 160, 200, 240, ...
The first number in both lists is 200.

Check: GCF × LCM = product

5 × 200 = 1,000 = 25 × 40. This always holds for two numbers, so you can find the LCM as (25 × 40) ÷ 5 = 200.

Simplifying the fraction 25/40

Divide the top and bottom by the GCF 5: 25/40 = 5/8.

GCF and LCM of similar pairs

See also: factors of 25 · factors of 40.

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