GCF and LCM of 16 and 28

The GCF of 16 and 28 is 4. The LCM of 16 and 28 is 112.

Method 1: list the factors (GCF)

Factors of 16: 1, 2, 4, 8, 16.
Factors of 28: 1, 2, 4, 7, 14, 28.
Common factors: 1, 2 and 4. The greatest of these is 4.

Method 2: prime factorization

16 = 2 × 2 × 2 × 2
28 = 2 × 2 × 7

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 × 2 × 7 = 112.

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 × 16 + 12
  2. 16 = 1 × 12 + 4
  3. 12 = 3 × 4 + 0

The last non-zero remainder is 4, so GCF(16, 28) = 4.

LCM by listing multiples

Multiples of 16: 16, 32, 48, 64, 80, 96, 112, 128, ...
Multiples of 28: 28, 56, 84, 112, 140, ...
The first number in both lists is 112.

Check: GCF × LCM = product

4 × 112 = 448 = 16 × 28. This always holds for two numbers, so you can find the LCM as (16 × 28) ÷ 4 = 112.

Simplifying the fraction 16/28

Divide the top and bottom by the GCF 4: 16/28 = 4/7.

GCF and LCM of similar pairs

NumbersGCFLCM
2 and 16216
3 and 16148
4 and 16416
5 and 16180
6 and 16248
7 and 161112
2 and 28228
3 and 28184
4 and 28428
5 and 281140
6 and 28284
7 and 28728

See also: factors of 16 · factors of 28.

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