GCF and LCM of 16 and 22

The GCF of 16 and 22 is 2. The LCM of 16 and 22 is 176.

• GCF (greatest common factor, also called GCD or HCF) of 16 and 22 = 2
• LCM (least common multiple) of 16 and 22 = 176

Method 1: list the factors (GCF)

Factors of 16: 1, 2, 4, 8, 16.
Factors of 22: 1, 2, 11, 22.
Common factors: 1 and 2. The greatest of these is 2.

Method 2: prime factorization

16 = 2 × 2 × 2 × 2
22 = 2 × 11

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 × 2 × 2 × 11 = 176.

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. 22 = 1 × 16 + 6
2. 16 = 2 × 6 + 4
3. 6 = 1 × 4 + 2
4. 4 = 2 × 2 + 0

The last non-zero remainder is 2, so GCF(16, 22) = 2.

LCM by listing multiples

Multiples of 16: 16, 32, 48, 64, 80, 96, 112, 128, 144, ...
Multiples of 22: 22, 44, 66, 88, 110, 132, 154, 176, 198, ...
The first number in both lists is 176.

Check: GCF × LCM = product

2 × 176 = 352 = 16 × 22. This always holds for two numbers, so you can find the LCM as (16 × 22) ÷ 2 = 176.

Simplifying the fraction 16/22

Divide the top and bottom by the GCF 2: 16/22 = 8/11.

GCF and LCM of similar pairs

See also: factors of 16 · factors of 22.

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