GCF and LCM of 29 and 100

The GCF of 29 and 100 is 1. The LCM of 29 and 100 is 2,900.

• GCF (greatest common factor, also called GCD or HCF) of 29 and 100 = 1
• LCM (least common multiple) of 29 and 100 = 2,900

29 and 100 share no common factor except 1, so they are coprime (relatively prime). When two numbers are coprime their LCM is simply their product: 29 × 100 = 2,900.

Method 1: list the factors (GCF)

Factors of 29: 1, 29.
Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100.
Common factors: 1. The greatest of these is 1.

Method 2: prime factorization

29 = 29 (prime)
100 = 2 × 2 × 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 × 5 × 5 × 29 = 2,900.

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. 100 = 3 × 29 + 13
2. 29 = 2 × 13 + 3
3. 13 = 4 × 3 + 1
4. 3 = 3 × 1 + 0

The last non-zero remainder is 1, so GCF(29, 100) = 1.

LCM by listing multiples

Multiples of 29: 29, 58, 87, 116, 145, 174, 203, 232, 261, ...
Multiples of 100: 100, 200, 300, 400, 500, 600, 700, 800, 900, ...
The first number in both lists is 2,900.

Check: GCF × LCM = product

1 × 2,900 = 2,900 = 29 × 100. This always holds for two numbers, so you can find the LCM as (29 × 100) ÷ 1 = 2,900.

Simplifying the fraction 29/100

29/100 is already in lowest terms because the GCF of 29 and 100 is 1.

GCF and LCM of similar pairs

See also: factors of 29 · factors of 100.

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