Pack 48 red and 72 blue cards into the greatest number of identical groups.
GCF(48, 72) = 24, so make 24 groups. Each group gets 2 red and 3 blue cards.
CALCULATE · UNDERSTAND · PRACTICE
GCF Calculator
Find the greatest common factor of 2–15 integers, then see why it works through prime powers, common factors, and every Euclidean division.
15numbers at once
3solution methods
exactinteger math
GREATEST COMMON FACTOR LAB
One answer, three ways to prove it
Signed integers and zero are accepted. The GCF is always reported as a non-negative divisor. Each magnitude is limited to unsigned 64-bit so prime-factor proofs stay deterministic.
GREATEST COMMON FACTOR12
GCF(24, 36, 48) = 12
LCM144
common factors6
relationshipshare factor 12
PRIME FACTORIZATION
2² × 3 = 12Keep the lowest shared exponent
EUCLIDEAN ALGORITHM
GCF = 12Divide, keep the remainder, repeat
FACTOR LISTING
1, 2, 3, 4, 6, 12The largest member of the common set
GCF IN ACTION
Reduce a ratio or fraction instantly
Use the same GCF to remove every shared factor at once.
:
divide both by 422 : 3
84 ÷ 42 : 126 ÷ 42
WORD-PROBLEM TRANSLATOR
When should you reach for the GCF?
Largest equal groups, biggest identical tiles, or longest equal cuts usually point to a greatest common factor.
DAILY 12
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GCF
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FOCUSED PRACTICE
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MIXED
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30sFactors method
List factors of each number, take the overlap, then choose the largest. Great for small values and for seeing what “common” means.
Prime-factor method
Factor each number into primes. For each prime shared by every number, keep only the smallest exponent.
Euclid method
For large values, repeated division is usually fastest: GCF(a,b) = GCF(b, a mod b).
GCF vs LCM
GCF asks for the largest size that divides everything. LCM asks for the smallest positive size that every input divides into.
Methods, exactness & scope
Exact integer arithmetic
Inputs are parsed with JavaScript BigInt. GCF, LCM, Euclidean steps, factor powers, common factors, and ratio reduction use integer arithmetic with no floating-point rounding.
Deterministic factor proofs
Prime-factor views use deterministic Miller–Rabin plus Pollard-rho within the declared unsigned 64-bit magnitude range. Negative signs do not change a positive GCF.
Why 15 inputs?
The main calculator intentionally supports 2–15 integers, matching the practical multi-value workflow while keeping the first screen readable on phones.