GCF and LCM of 10 and 16

The GCF of 10 and 16 is 2. The LCM of 10 and 16 is 80.

Method 1: list the factors (GCF)

Factors of 10: 1, 2, 5, 10.
Factors of 16: 1, 2, 4, 8, 16.
Common factors: 1 and 2. The greatest of these is 2.

Method 2: prime factorization

10 = 2 × 5
16 = 2 × 2 × 2 × 2

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 × 5 = 80.

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

The last non-zero remainder is 2, so GCF(10, 16) = 2.

LCM by listing multiples

Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, ...
Multiples of 16: 16, 32, 48, 64, 80, 96, ...
The first number in both lists is 80.

Check: GCF × LCM = product

2 × 80 = 160 = 10 × 16. This always holds for two numbers, so you can find the LCM as (10 × 16) ÷ 2 = 80.

Simplifying the fraction 10/16

Divide the top and bottom by the GCF 2: 10/16 = 5/8.

GCF and LCM of similar pairs

NumbersGCFLCM
2 and 10210
3 and 10130
4 and 10220
5 and 10510
6 and 10230
7 and 10170
2 and 16216
3 and 16148
4 and 16416
5 and 16180
6 and 16248
7 and 161112

See also: factors of 10 · factors of 16 · 10/16 as a decimal.

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