What is the GCF of 16 and 30?

The greatest common factor of 16 and 30 is 2.

What is the LCM of 16 and 30?

The least common multiple of 16 and 30 is 240.

Are 16 and 30 coprime?

No. They share the common factor 2, and their GCF is 2.

GCF and LCM of 16 and 30

The GCF of 16 and 30 is 2. The LCM of 16 and 30 is 240.

GCF (greatest common factor, also called GCD or HCF) of 16 and 30 = 2
LCM (least common multiple) of 16 and 30 = 240

Method 1: list the factors (GCF)

Factors of 16: 1, 2, 4, 8, 16.
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30.
Common factors: 1 and 2. The greatest of these is 2.

Method 2: prime factorization

16 = 2 × 2 × 2 × 2
30 = 2 × 3 × 5

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 × 3 × 5 = 240.

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.

30 = 1 × 16 + 14
16 = 1 × 14 + 2
14 = 7 × 2 + 0

The last non-zero remainder is 2, so GCF(16, 30) = 2.

LCM by listing multiples

Multiples of 16: 16, 32, 48, 64, 80, 96, 112, 128, 144, ...
Multiples of 30: 30, 60, 90, 120, 150, 180, 210, 240, 270, ...
The first number in both lists is 240.

Check: GCF × LCM = product

2 × 240 = 480 = 16 × 30. This always holds for two numbers, so you can find the LCM as (16 × 30) ÷ 2 = 240.

Simplifying the fraction 16/30

Divide the top and bottom by the GCF 2: 16/30 = 8/15.

GCF and LCM of similar pairs

Numbers	GCF	LCM
2 and 16	2	16
3 and 16	1	48
4 and 16	4	16
5 and 16	1	80
6 and 16	2	48
7 and 16	1	112
2 and 30	2	30
3 and 30	3	30
4 and 30	2	60
5 and 30	5	30
6 and 30	6	30
7 and 30	1	210

See also: factors of 16 · factors of 30.

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