GCF and LCM of 25 and 28

The GCF of 25 and 28 is 1. The LCM of 25 and 28 is 700.

• GCF (greatest common factor, also called GCD or HCF) of 25 and 28 = 1
• LCM (least common multiple) of 25 and 28 = 700

25 and 28 share no common factor except 1, so they are coprime (relatively prime). When two numbers are coprime their LCM is simply their product: 25 × 28 = 700.

Method 1: list the factors (GCF)

Factors of 25: 1, 5, 25.
Factors of 28: 1, 2, 4, 7, 14, 28.
Common factors: 1. The greatest of these is 1.

Method 2: prime factorization

25 = 5 × 5
28 = 2 × 2 × 7

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 × 5 × 5 × 7 = 700.

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 × 25 + 3
2. 25 = 8 × 3 + 1
3. 3 = 3 × 1 + 0

The last non-zero remainder is 1, so GCF(25, 28) = 1.

LCM by listing multiples

Multiples of 25: 25, 50, 75, 100, 125, 150, 175, 200, 225, ...
Multiples of 28: 28, 56, 84, 112, 140, 168, 196, 224, 252, ...
The first number in both lists is 700.

Check: GCF × LCM = product

1 × 700 = 700 = 25 × 28. This always holds for two numbers, so you can find the LCM as (25 × 28) ÷ 1 = 700.

Simplifying the fraction 25/28

25/28 is already in lowest terms because the GCF of 25 and 28 is 1.

GCF and LCM of similar pairs

See also: factors of 25 · factors of 28.

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