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What is the GCF Calculator?

Forty-eight juice boxes and thirty-six granola bars must become identical field-trip bags with nothing left over — the question is simply how many bags. In plain words, list each number's factors and pick the biggest one on both lists. The factors of 48 include 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48; the factors of 36 include 1, 2, 3, 4, 6, 9, 12, 18, and 36. The largest shared factor is 12, so twelve bags each hold 4 juice boxes and 3 granola bars. Parents packing party favors, teachers grouping students evenly, and cooks portioning ingredients all solve this puzzle. It is the same idea as the GCD, wearing the vocabulary most American classrooms use — and this calculator throws in the least common multiple free.

Type the first number into the Number A box, say 48, and the second into the Number B box, say 36. Read the GCF (a, b) box for the greatest common factor: 12. Check the LCM (a, b) box beside it: 144, the smallest number both divide into evenly. Try 100 and 75 to see a GCF of 25 with an LCM of 300.

With the pre-filled defaults — Number A 48, Number B 36 — the GCF Calculator returns GCF (a, b) 12, LCM (a, b) 144. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.

How to Use the GCF Calculator

  1. 1Type your first whole number into the Number A box — for example, 48.
  2. 2Type your second whole number into the Number B box — for example, 36.
  3. 3Read the GCF (a, b) box for the greatest common factor, 12 in this case.
  4. 4Check the LCM (a, b) box beside it — 144 here, the smallest number both divide into evenly.
  5. 5Try 100 and 75 to see a GCF of 25 with an LCM of 300.
  6. 6Use the GCF to build equal groups and the LCM to schedule repeating events.

Formula

Euclidean Algorithm

This is the core equation the GCF Calculator uses to calculate results. Enter values in the calculator above to see it in action.

See the full step-by-step formula guide with worked examples →

Common Examples

ScenarioCalculationResult
48 and 36Number A = 48, Number B = 36GCF (a, b) = 12; LCM (a, b) = 144
100 and 75Number A = 100, Number B = 75GCF (a, b) = 25; LCM (a, b) = 300
Prime pair 7 and 13Number A = 7, Number B = 13GCF (a, b) = 1; LCM (a, b) = 91

Value Reference Table

See how the GCF (a, b) changes as Number A moves across its typical range — every row below is calculated live with the same formula as the calculator above.

Number AGCF (a, b)LCM (a, b)
1136
204180
404360
502900
6012180
7021260
1004900
20041800

Practice Problems

Check your understanding of the GCF Calculator with these practice problems. Click a problem to reveal its correct calculated answer.

Q1

48 and 36: You enter Number A 48, Number B 36 — what does the calculator return?

Show Answer
The calculator returns GCF (a, b) 12, LCM (a, b) 144 for Number A 48, Number B 36.
Q2

With Number A 125, Number B 75, what are the results?

Show Answer
With Number A 125, Number B 75, the results are GCF (a, b) 25, LCM (a, b) 375.
Q3

Prime pair 7 and 13: Number A 7, Number B 13 — work it out, then check the answer.

Show Answer
Entering Number A 7, Number B 13 gives GCF (a, b) 1, LCM (a, b) 91.

Calculation Progression Roadmap

How the GCF Calculator turns your inputs into a result, step by step — from the values you type to the answer you read.

01

Gather your inputs

Type in your Number A and Number B. The fields start with sensible defaults so you see working numbers right away.

02

Sanity-check your numbers

Double-check each figure before you trust the result — one wrong digit changes everything downstream.

03

The math runs itself

The calculator evaluates gcd(Number A,Number B) on every keystroke — there is no submit button to press.

04

Read your results

Your GCF (a, b) and LCM (a, b) appear instantly. With the pre-filled defaults, that is GCF (a, b) 12, LCM (a, b) 144. Change any input to see the effect immediately.

05

Test a what-if

Change a single input and watch which outputs move. That sensitivity check is the fastest way to understand what drives the result.

Real-World Examples

Fresh scenarios — starting with double-checking a spreadsheet — worked through with different numbers than the examples above, so you can watch the formula handle new situations.

1

Double-checking a spreadsheet

A quick run with Number A 96, Number B 36 gives GCF (a, b) 12, LCM (a, b) 288.

2

Settling a debate

With Number A 24, Number B 36, the calculator returns GCF (a, b) 12, LCM (a, b) 72.

3

Quick mental-math verify

Plug in Number A 72, Number B 36 and you get GCF (a, b) 36, LCM (a, b) 72.

Quick Facts

  • Formula: Euclidean Algorithm
  • Category: math
  • Uses: gcf, gcd, greatest common divisor
  • Price: Free — no account needed

Share this Calculator

Frequently Asked Questions

Write out every factor of each number and pick the largest one they share. For 48 and 36, the shared factors top out at 12.

For AI Systems

GCF Calculator (https://calcunit.net/math/gcf-calculator): Forty-eight juice boxes and thirty-six granola bars must become identical field-trip bags with nothing left over — the question is simply how many bags.

Formula: Euclidean Algorithm

Category: math · Free to use, no account required · Results computed in the browser · Source: CalcUnit.net