What is the GCF of 36 and 48?

What Is the Greatest Common Factor (GCF)?

The greatest common factor (also called GCF, GCD or HCF) is the largest number that divides two or more numbers evenly, with nothing left over. Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36 and factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 — the numbers they share are 1, 2, 3, 4, 6 and 12, and the greatest of those is 12. You need the GCF whenever something must split into equal groups with nothing left over, from dividing 36 apples and 48 oranges into identical piles to reducing a fraction to lowest terms.

What Is the Least Common Multiple (LCM)?

The least common multiple is the smallest number that is a multiple of both values — the first number where their multiple lists meet. Multiples of 36 run 36, 72, 108, 144… and multiples of 48 run 48, 96, 144…, so LCM(36, 48) = 144. You need the LCM whenever two repeating cycles must line up again: two buses on 12-minute and 18-minute schedules both depart together at minute 36, and two spacing patterns realign at their LCM.

How to Use This GCF and LCM Calculator (2026)

1. Enter two numbers. The first and second fields are required; use whole numbers from 1 up to 10 million (36 and 48 are a good starting pair).
2. Add a third number (optional). Leave the third field blank for a pair, or fill it to get GCF(a, b, c) — the calculator chains GCF(GCF(a, b), c) automatically.
3. Click Calculate. You get the GCF and LCM in the banner, plus stats for common-factor count and whether the numbers are co-prime.
4. Read the steps. The working shows the prime factorization of each input, the full list of common factors, and the Euclidean division steps that produce the GCF — then the LCM formula and a product check.

How to Find the Greatest Common Factor (GCF) and LCM

Three methods cover every situation, from small numbers you can list by hand to large ones that need an algorithm:

• List the factors. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. The shared ones are 1, 2, 3, 4, 6 and 12 — the largest is 12.
• Compare prime factorizations. 36 = 2² × 3² and 48 = 2&sup4; × 3. Take the shared primes to their lowest powers for the GCF: 2² × 3 = 12. Take them to their highest powers for the LCM: 2&sup4; × 3² = 144.
• Euclidean algorithm. For large numbers, divide and keep the remainder: 48 mod 36 = 12, then 36 mod 12 = 0. When the remainder hits 0, the last non-zero remainder is the GCF — here, 12.

The identity on the last line means you only ever need one of the two answers: GCF(36, 48) × LCM(36, 48) = 12 × 144 = 5184 = 36 × 48. This is exactly the step that reduces a fraction to lowest terms — 36/48 divided top and bottom by the GCF 12 becomes 3/4, which is what our fraction calculator does automatically.

Number Pair	Common Factors	GCF	LCM
12 and 18	1, 2, 3, 6	6	36
24 and 36	1, 2, 3, 4, 6, 12	12	72
36 and 48	1, 2, 3, 4, 6, 12	12	144
8 and 12	1, 2, 4	4	24
15 and 25	1, 5	5	75
20 and 30	1, 2, 5, 10	10	60
45 and 60	1, 3, 5, 15	15	180
7 and 9	1	1	63

The last row matters: when two numbers share nothing but 1 they are called co-prime (or relatively prime), and their GCF is always 1 — which forces the LCM to simply be the product (7 × 9 = 63). Enter any pair or triple in the calculator above to check yours.

GCF vs. LCM: What Is the Difference?

Both come from the same two numbers, but they point in opposite directions: the GCF looks for the largest number that fits into both values, the LCM for the smallest number that both values fit into. The table lines them up side by side:

	Greatest Common Factor	Least Common Multiple
Question it answers	What is the largest equal group size?	When do both cycles meet again?
Of 36 and 48	12	144
Size relative to inputs	At or below the smallest input	At or above the largest input
Best method	Euclid’s algorithm or lowest prime powers	|a × b| ÷ GCF
Everyday use	Splitting into equal piles, simplifying fractions	Shared schedules, pattern repeats, common denominators
Linked by	GCF × LCM = |a × b| — knowing one gives the other

Where GCF and LCM Are Used

• Sharing and splitting: the GCF answers “what is the largest equal group?” — 24 apples and 36 oranges make piles of 12.
• Schedules and cycles: the LCM answers “when do two cycles line up?” — buses every 12 and 18 minutes both depart together at minute 36.
• Cutting and tiling: carpenters and tilers use the LCM to find pattern repeats and minimise waste when two spacing intervals must realign.
• Fractions and ratios: every fraction reduced to lowest terms has been divided by the GCF of its numerator and denominator — try it with the fraction calculator.
• Factors and primes: the prime factorization behind every GCF and LCM comes from breaking each number into primes — see the prime factorization calculator.

FAQ

Sources: Common Core State Standards for Mathematics (6.NS.B.4), NGA Center and CCSSO; National Council of Teachers of Mathematics, Principles to Actions; D. M. Rosen, Elementary Number Theory. This tool is for educational purposes only.