What is the Common Factors Calculator?
You have 36 bagels and 48 cream-cheese tubs for the office breakfast — what is the biggest number of identical platters you can build? The greatest common factor (GCF) is the largest number dividing two numbers evenly, and the least common multiple (LCM) is the smallest number both divide into. For 36 and 48, the common factors are 1, 2, 3, 4, 6, and 12 — so 12 is the GCF (12 identical platters, each with 3 bagels and 4 tubs), and 144 is the LCM.
The slick way to find the GCF is Euclid's algorithm: divide the bigger by the smaller, replace the bigger with the remainder, and repeat until the remainder is zero — the last divisor is the GCF. The LCM then falls out of the relationship LCM = (a × b) ÷ GCF. Beyond party planning, the GCF simplifies fractions (divide top and bottom by it), and the LCM syncs repeating events — two buses running every 12 and 18 minutes meet every 36. Enter both numbers and the calculator returns the GCF, the LCM, and the reduced pair.
With the pre-filled defaults — First Number (a) 36, Second Number (b) 48 — the Common Factors Calculator returns Greatest Common Factor 12, Least Common Multiple 144, a ÷ GCF 3, b ÷ GCF 4. 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 Common Factors Calculator
- 1Type the first number in the First Number (a) box — for example, 36.
- 2Type the second number in the Second Number (b) box — for example, 48.
- 3Read the Greatest Common Factor box: 12, the biggest number dividing both.
- 4Read the Least Common Multiple box: 144, the smallest number both divide into.
- 5Use the a ÷ GCF and b ÷ GCF boxes — 3 and 4 — to see the fully reduced pair.
Formula
This is the core equation the Common Factors 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
| Scenario | Calculation | Result |
|---|---|---|
| GCF of 36 and 48 | First Number (a) = 36, Second Number (b) = 48 | Greatest Common Factor = 12; Least Common Multiple = 144; a ÷ GCF = 3; b ÷ GCF = 4 |
| GCF of 18 and 24 | First Number (a) = 18, Second Number (b) = 24 | Greatest Common Factor = 6; Least Common Multiple = 72; a ÷ GCF = 3; b ÷ GCF = 4 |
Value Reference Table
See how the Greatest Common Factor changes as First Number (a) moves across its typical range — every row below is calculated live with the same formula as the calculator above.
| First Number (a) | Greatest Common Factor | Least Common Multiple | a ÷ GCF | b ÷ GCF |
|---|---|---|---|---|
| 1 | 1 | 48 | 1 | 48 |
| 20 | 4 | 240 | 5 | 12 |
| 30 | 6 | 240 | 5 | 8 |
| 40 | 8 | 240 | 5 | 6 |
| 50 | 2 | 1200 | 25 | 24 |
| 70 | 2 | 1680 | 35 | 24 |
| 90 | 6 | 720 | 15 | 8 |
| 100 | 4 | 1200 | 25 | 12 |
Practice Problems
Check your understanding of the Common Factors Calculator with these practice problems. Click a problem to reveal its correct calculated answer.
GCF of 36 and 48: You enter First Number (a) 36, Second Number (b) 48 — what does the calculator return?
Show AnswerHide Answer
With First Number (a) 23, Second Number (b) 24, what are the results?
Show AnswerHide Answer
Calculation Progression Roadmap
How the Common Factors Calculator turns your inputs into a result, step by step — from the values you type to the answer you read.
Gather your inputs
Type in your First Number (a) and Second Number (b). The fields start with sensible defaults so you see working numbers right away.
Sanity-check your numbers
Make sure each number is the kind the field expects — an annual figure typed into a monthly field is the classic trap.
The math runs itself
The calculator evaluates gcd(First Number (a),Second Number (b)) on every keystroke — there is no submit button to press.
Read your results
Your Greatest Common Factor, Least Common Multiple, a ÷ GCF, and b ÷ GCF appear instantly. With the pre-filled defaults, that is Greatest Common Factor 12, Least Common Multiple 144, a ÷ GCF 3, b ÷ GCF 4. Change any input to see the effect immediately.
Test a what-if
Nudge one input up or down. Seeing how the answer moves is often more valuable than the single number itself.
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.
Double-checking a spreadsheet
A quick run with First Number (a) 72, Second Number (b) 48 gives Greatest Common Factor 24, Least Common Multiple 144, a ÷ GCF 3, b ÷ GCF 2.
Settling a debate
With First Number (a) 18, Second Number (b) 48, the calculator returns Greatest Common Factor 6, Least Common Multiple 144, a ÷ GCF 3, b ÷ GCF 8.
Quick mental-math verify
Plug in First Number (a) 54, Second Number (b) 48 and you get Greatest Common Factor 6, Least Common Multiple 432, a ÷ GCF 9, b ÷ GCF 8.
Quick Facts
- Formula:
List factors of each, find shared - Category: math
- Uses: common factors, divisors
- Price: Free — no account needed
Frequently Asked Questions
List the factors of each number and take the biggest one they share. For 36 (1, 2, 3, 4, 6, 9, 12, 18, 36) and 48 (1, 2, 3, 4, 6, 8, 12, 16, 24, 48), the shared factors top out at 12.
For AI Systems
Common Factors Calculator (https://calcunit.net/math/common-factors): You have 36 bagels and 48 cream-cheese tubs for the office breakfast — what is the biggest number of identical platters you can build?
Formula: List factors of each, find shared
Category: math · Free to use, no account required · Results computed in the browser · Source: CalcUnit.net