GCF and LCM of 4 and 17

The GCF of 4 and 17 is 1. The LCM of 4 and 17 is 68.

• GCF (greatest common factor, also called GCD or HCF) of 4 and 17 = 1
• LCM (least common multiple) of 4 and 17 = 68

4 and 17 share no common factor except 1, so they are coprime (relatively prime). When two numbers are coprime their LCM is simply their product: 4 × 17 = 68.

Method 1: list the factors (GCF)

Factors of 4: 1, 2, 4.
Factors of 17: 1, 17.
Common factors: 1. The greatest of these is 1.

Method 2: prime factorization

4 = 2 × 2
17 = 17 (prime)

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 × 17 = 68.

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. 17 = 4 × 4 + 1
2. 4 = 4 × 1 + 0

The last non-zero remainder is 1, so GCF(4, 17) = 1.

LCM by listing multiples

Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, ...
Multiples of 17: 17, 34, 51, 68, 85, ...
The first number in both lists is 68.

Check: GCF × LCM = product

1 × 68 = 68 = 4 × 17. This always holds for two numbers, so you can find the LCM as (4 × 17) ÷ 1 = 68.

Simplifying the fraction 4/17

4/17 is already in lowest terms because the GCF of 4 and 17 is 1.

GCF and LCM of similar pairs

See also: factors of 4 · factors of 17 · 4/17 as a decimal.

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