GCF and LCM of 16 and 25

The GCF of 16 and 25 is 1. The LCM of 16 and 25 is 400.

• GCF (greatest common factor, also called GCD or HCF) of 16 and 25 = 1
• LCM (least common multiple) of 16 and 25 = 400

16 and 25 share no common factor except 1, so they are coprime (relatively prime). When two numbers are coprime their LCM is simply their product: 16 × 25 = 400.

Method 1: list the factors (GCF)

Factors of 16: 1, 2, 4, 8, 16.
Factors of 25: 1, 5, 25.
Common factors: 1. The greatest of these is 1.

Method 2: prime factorization

16 = 2 × 2 × 2 × 2
25 = 5 × 5

GCF: multiply the prime factors both numbers share: there are none, so the GCF is 1.

LCM: multiply every prime the maximum number of times it appears in either number: 2 × 2 × 2 × 2 × 5 × 5 = 400.

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. 25 = 1 × 16 + 9
2. 16 = 1 × 9 + 7
3. 9 = 1 × 7 + 2
4. 7 = 3 × 2 + 1
5. 2 = 2 × 1 + 0

The last non-zero remainder is 1, so GCF(16, 25) = 1.

LCM by listing multiples

Multiples of 16: 16, 32, 48, 64, 80, 96, 112, 128, 144, ...
Multiples of 25: 25, 50, 75, 100, 125, 150, 175, 200, 225, ...
The first number in both lists is 400.

Check: GCF × LCM = product

1 × 400 = 400 = 16 × 25. This always holds for two numbers, so you can find the LCM as (16 × 25) ÷ 1 = 400.

Simplifying the fraction 16/25

16/25 is already in lowest terms because the GCF of 16 and 25 is 1.

GCF and LCM of similar pairs

See also: factors of 16 · factors of 25 · 16/25 as a decimal.

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