GCF and LCM of 22 and 28

The GCF of 22 and 28 is 2. The LCM of 22 and 28 is 308.

• GCF (greatest common factor, also called GCD or HCF) of 22 and 28 = 2
• LCM (least common multiple) of 22 and 28 = 308

Method 1: list the factors (GCF)

Factors of 22: 1, 2, 11, 22.
Factors of 28: 1, 2, 4, 7, 14, 28.
Common factors: 1 and 2. The greatest of these is 2.

Method 2: prime factorization

22 = 2 × 11
28 = 2 × 2 × 7

GCF: multiply the prime factors both numbers share: 2 = 2.

LCM: multiply every prime the maximum number of times it appears in either number: 2 × 2 × 7 × 11 = 308.

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. 28 = 1 × 22 + 6
2. 22 = 3 × 6 + 4
3. 6 = 1 × 4 + 2
4. 4 = 2 × 2 + 0

The last non-zero remainder is 2, so GCF(22, 28) = 2.

LCM by listing multiples

Multiples of 22: 22, 44, 66, 88, 110, 132, 154, 176, 198, ...
Multiples of 28: 28, 56, 84, 112, 140, 168, 196, 224, 252, ...
The first number in both lists is 308.

Check: GCF × LCM = product

2 × 308 = 616 = 22 × 28. This always holds for two numbers, so you can find the LCM as (22 × 28) ÷ 2 = 308.

Simplifying the fraction 22/28

Divide the top and bottom by the GCF 2: 22/28 = 11/14.

GCF and LCM of similar pairs

See also: factors of 22 · factors of 28.

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