Greatest Common Divisor (GCD) calculator - solves GCD for given numbers. Displays all prime dividers (in a school-like way), so you know how the solution can be found. It can find the GCD for up to 10 numbers at once !

Enter your numbers here#

Results: factorization step-by-step#

Number #1

Number #2

31752

36
18
9
3
1

2
2
3
3

31752
15876
7938
3969
1323
441
147
49
7
1

2
2
2
3
3
3
3
7
7

Results: podsumowanie#

Detected numbers
Numbers you entered without duplicates	36, 31752
GCD
Greatest Common Divisor (GCD)	36
GCD prime factors	2² × 3²
Are coprime integers	no ✗
LCM
Least common multiple (LCM)	31752
LCM prime factors	2³ × 3⁴ × 7²
Other
Processing time (performance)	1ms

Common sense tells#

The factors of 36 are: 1, 4, 6, 9, 12, 18, 36.

The factors of 31752 are: 1, 4, 6, 8, 9, 12, 14, 18, 21, 24, 27, 28, 36, 42, 49, 54, 56, 63, 72, 81, 84, 98, 108, 126, 147, 162, 168, 189, 196, 216, 252, 294, 324, 378, 392, 441, 504, 567, 588, 648, 756, 882, 1134, 1176, 1323, 1512, 1764, 2268, 2646, 3528, 3969, 4536, 5292, 7938, 10584, 15876, 31752.

The greatest common divisor (factor) is 36.

Some facts#

Greatest common divisor (in short: GCD) is the largest positive integer that divides two or more numbers without remainder.
Greatest common divisor is also known as greatest common factor (in short: (GCF) and highest common factor (HCF) (in short: HCF).
The greatest common divisor of the numbers a and b is usually denoted by GCD(a, b) or gcd(a, b).

$\text{GCD}(a, b) = \text{greatest common divisor of numbers} \left\{a, b\right\}$
The greatest common divisor can also be determined for more numbers e.g. GCD(4, 6, 12) is 3 because it is the largest number by which all three numbers are divisible.

$\text{GCD}(a, b, c, ...) = \text{greatest common divisor of numbers} \left\{a, b, c, ... \right\}$
The greatest common divisor is used, for example, in operations on fractions, e.g. to shorten them. To get the simplest fraction (shortened), we divide the numerator and denominator by GCD of the numerator and denominator.

ⓘ Example: Let's take a fraction 4/6 (four sixths). The numerator is 4 and the denominator is 6. GCD of 4 and 6 is 2, so we divide the numerator and the denominator by 2 and the fraction 2/3 (two thirds) comes out, which is the simplest, non-abbreviated form of this fraction.
$\dfrac{4}{6} = \dfrac{2 \times \cancel{2}} {3 \times \cancel{2}} = \dfrac{2}{3}$

ⓘ Hint: If you want to learn more about shortening fractions, check out our other calculator: Fractions.
Two numbers for which greatest common divisor is one are called coprime integers. This definition can be generalized to any amount of numbers. The below formula means that the numbers $\left\{a, b, c, ... \right\}$ are coprime:

$\text{GCD}(a, b, c, ...) = 1$
A property similar to GCD is the least common multiple (in short: LCM), which is the smallest natural number divisible by each of the given numbers.

ⓘ Hint: If you want to learn more about LCM, check out our other calculator: LCM.
A property similar to LCM is the greatest common divisor (in short: GCD), which is the largest natural number by which all of the given numbers are divisible.

ⓘ Hint: If you want to learn more about GCD check out our other calculator: GCD.
If we have GCD for a pair of numbers, we can use it to calculate LCM and vice versa using the following formula. Unfortunately, it works only for a pair of numbers, i.e. it can't be generalized to more than 2 numbers.

$\text{GCD}(a, b) = \dfrac{a \times b} {\text{LCM}(a, b)}$

How to use this tool#

To search for greatest common divisor or least common multiplier enter your numbers into input box.
You can enter any amount of integer numbers.
All numbers should be non-zero integer (so you can use negative numbers).

Tags and links to this website#

Tags:

greatest_common_divisor · gcd · greatest_common_factor · highest_common_factor

Tags to Polish version:

najwiekszy_wspolny_dzielnik · nwd

What tags this calculator has#

CALCULATOR · MATH · A -> Z (all)

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Links to external sites (leaving Calculla?)#

Ancient version of this site - links#

In December 2016 the Calculla website has been republished using new technologies and all calculators have been rewritten. Old version of the Calculla is still available through this link: v1.calculla.com. We left the version 1 of Calculla untouched for archival purposes.
Direct link to the old version: "Calculla v1" version of this calculator