Most scientific and graphing calculators have a built-in GCD function that finds the greatest common factor of two numbers in seconds. The exact button sequence depends on your calculator brand and model, but the function is usually tucked inside a math or number submenu rather than printed on a key you can see.
Finding GCF on a TI-84 or TI-84 Plus CE
Texas Instruments graphing calculators include a function called gcd( located in the MATH menu. Here’s the exact sequence:
- Press the MATH button.
- Arrow right to the NUM submenu.
- Scroll down to 9:gcd( and press ENTER.
- Type your two numbers separated by a comma. For example:
gcd(28,35). - Press ENTER to get the result.
For gcd(28,35), the calculator returns 7. This works the same way on the TI-83, TI-84 Plus, and TI-84 Plus CE. On older TI models, the gcd function may appear at a different position in the NUM submenu, but the menu path is the same: MATH, then NUM, then gcd.
If you need the GCF of more than two numbers, run the function in stages. Find the GCF of the first two numbers, then find the GCF of that result and the third number. For example, to find the GCF of 24, 36, and 60: first calculate gcd(24,36), which gives 12, then calculate gcd(12,60), which gives 12. That’s your final answer.
Finding GCF on a Casio Scientific Calculator
Casio’s popular fx-series scientific calculators (like the fx-115ES Plus and fx-991ES Plus C) have a dedicated GCD function. The steps are straightforward:
- Press the FUNCTION or CATALOG key (this varies by model) to access the function menu.
- Select GCD from the list.
- Enter your first number, press the comma key, then enter your second number.
- Press = to see the result.
Using the earlier example, entering GCD 28, 35 returns 7. Some Casio models require you to navigate through an on-screen menu to find GCD, while others place it behind a SHIFT or ALPHA key combination. Check the label printed above the keys on your specific model, since Casio often places secondary functions there in small text.
Finding GCF on a Phone or Online Calculator
If you don’t have a scientific calculator handy, the built-in calculators on phones won’t have a GCF button. But you have quick alternatives. Typing “GCF of 28 and 35” into Google’s search bar returns the answer directly. Wolfram Alpha, Symbolab, and similar math sites also accept GCF queries and show the work if you need to see the steps for a homework problem.
How to Find GCF on a Basic Calculator
A basic calculator with only addition, subtraction, multiplication, and division can still get you to the GCF. You just need to do the work manually using a method called the Euclidean algorithm. It sounds technical, but it boils down to repeated division.
Here’s how it works, using 48 and 18 as an example:
- Divide the larger number by the smaller: 48 ÷ 18 = 2 with a remainder of 12.
- Replace the larger number with the smaller, and the smaller with the remainder: now you’re working with 18 and 12.
- Divide again: 18 ÷ 12 = 1 with a remainder of 6.
- Replace again: now you’re working with 12 and 6.
- Divide again: 12 ÷ 6 = 2 with a remainder of 0.
- When the remainder hits zero, the last divisor (6) is your GCF.
On a basic calculator, you can find the remainder by dividing, ignoring the decimal part, multiplying the whole number result back by the divisor, and subtracting from the original. For the first step above: 48 ÷ 18 = 2.666…, so the whole number quotient is 2. Then 2 × 18 = 36, and 48 − 36 = 12. That 12 is your remainder.
This method works for any pair of numbers, no matter how large, and it converges quickly. Even numbers in the hundreds or thousands usually take only four or five rounds of division to reach a remainder of zero.
Quick Shortcut for Small Numbers
If both numbers are small enough that you can spot their factors, skip the calculator entirely. List the factors of each number and pick the largest one they share. For 28 (factors: 1, 2, 4, 7, 14, 28) and 35 (factors: 1, 5, 7, 35), the largest shared factor is 7. This approach gets tedious past two-digit numbers, which is exactly when the calculator’s built-in function or the Euclidean algorithm saves real time.