GCF and LCM of 16 and 26

The GCF of 16 and 26 is 2. The LCM of 16 and 26 is 208.

• GCF (greatest common factor, also called GCD or HCF) of 16 and 26 = 2
• LCM (least common multiple) of 16 and 26 = 208

Method 1: list the factors (GCF)

Factors of 16: 1, 2, 4, 8, 16.
Factors of 26: 1, 2, 13, 26.
Common factors: 1 and 2. The greatest of these is 2.

Method 2: prime factorization

16 = 2 × 2 × 2 × 2
26 = 2 × 13

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 × 13 = 208.

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. 26 = 1 × 16 + 10
2. 16 = 1 × 10 + 6
3. 10 = 1 × 6 + 4
4. 6 = 1 × 4 + 2
5. 4 = 2 × 2 + 0

The last non-zero remainder is 2, so GCF(16, 26) = 2.

LCM by listing multiples

Multiples of 16: 16, 32, 48, 64, 80, 96, 112, 128, 144, ...
Multiples of 26: 26, 52, 78, 104, 130, 156, 182, 208, 234, ...
The first number in both lists is 208.

Check: GCF × LCM = product

2 × 208 = 416 = 16 × 26. This always holds for two numbers, so you can find the LCM as (16 × 26) ÷ 2 = 208.

Simplifying the fraction 16/26

Divide the top and bottom by the GCF 2: 16/26 = 8/13.

GCF and LCM of similar pairs

See also: factors of 16 · factors of 26.

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