GCF and LCM of 28 and 40

The GCF of 28 and 40 is 4. The LCM of 28 and 40 is 280.

• GCF (greatest common factor, also called GCD or HCF) of 28 and 40 = 4
• LCM (least common multiple) of 28 and 40 = 280

Method 1: list the factors (GCF)

Factors of 28: 1, 2, 4, 7, 14, 28.
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40.
Common factors: 1, 2 and 4. The greatest of these is 4.

Method 2: prime factorization

28 = 2 × 2 × 7
40 = 2 × 2 × 2 × 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 × 7 = 280.

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 × 28 + 12
2. 28 = 2 × 12 + 4
3. 12 = 3 × 4 + 0

The last non-zero remainder is 4, so GCF(28, 40) = 4.

LCM by listing multiples

Multiples of 28: 28, 56, 84, 112, 140, 168, 196, 224, 252, ...
Multiples of 40: 40, 80, 120, 160, 200, 240, 280, 320, ...
The first number in both lists is 280.

Check: GCF × LCM = product

4 × 280 = 1,120 = 28 × 40. This always holds for two numbers, so you can find the LCM as (28 × 40) ÷ 4 = 280.

Simplifying the fraction 28/40

Divide the top and bottom by the GCF 4: 28/40 = 7/10.

GCF and LCM of similar pairs

See also: factors of 28 · factors of 40.

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