How this instrument works
Greatest common factor, GCF, is the largest whole number that divides evenly into two others. Applied here to a fraction, it is found from the numerator and denominator specifically, not from two interchangeable numbers picked at random: GCF = gcd(numerator, denominator). Once found, dividing both the top and bottom by that shared factor produces the smallest whole-number version of the exact same fraction, with nothing left over to reduce further.
A generic factor-finding tool elsewhere on this site takes any two whole numbers and stops once it reports their shared divisor, with no particular meaning attached to which number came first. This page is anchored to one job only: a fraction, where the top and bottom play fixed, unequal roles, and the point of finding their shared factor is to immediately divide it back out of both, arriving at Simplified numerator and Simplified denominator rather than stopping at the divisor alone.
It is also a narrower job than simplifying a ratio. A ratio such as 8:3 compares two separate quantities side by side, while a fraction such as 8⁄3 represents one quantity being divided by another — the arithmetic for reducing either happens to match, but the meaning attached to the two numbers differs. A genuine edge case worth flagging: when the GCF turns out to equal the denominator itself, the simplified denominator becomes 1, and what looked like a fraction turns out to be a whole number wearing a disguise.
- Enter the top number of your fraction into the Fraction numerator field.
- Enter the bottom number into the Fraction denominator field.
- Read Greatest common factor: the largest whole number dividing both evenly.
- Read Simplified numerator and Simplified denominator together: that pair is the same fraction in its lowest terms.
Worked example — simplifying the fraction 12⁄18
Twelve slices out of a batch of eighteen is the fraction 12⁄18. The greatest common factor of 12 and 18 is 6, so dividing both parts by 6 gives a simplified numerator of 12 ⁄ 6 = 2 and a simplified denominator of 18 ⁄ 6 = 3 — the fraction 2⁄3, the same proportion in its smallest whole-number form, with nothing further to reduce.
Not every fraction has that much room to shrink. Take 7⁄5: its GCF is exactly 1, meaning 7 and 5 already share no factor beyond the trivial one, so the fraction stays 7⁄5 unchanged. At the other extreme, 100⁄25 has a GCF of 25, and dividing both parts by it collapses the fraction all the way down to 4⁄1 — a whole number, 4, still technically wearing fraction clothing.
Questions
What is the GCF of a fraction?
It is the largest whole number that divides evenly into both the numerator and the denominator of that specific fraction. Dividing both parts by that number produces the smallest possible equivalent fraction, since nothing larger than the GCF could divide both cleanly without leaving a remainder.
How is this different from a generic GCD calculator?
A generic divisor tool treats its two inputs as interchangeable numbers and stops once it names their shared factor. This page instead treats the two inputs as a fraction's numerator and denominator specifically, and carries the result one step further by dividing it back into both parts to hand back an already-simplified fraction.
Isn't simplifying a fraction the same as simplifying a ratio?
The arithmetic matches, but the meaning differs. A ratio such as 8:3 compares two separate quantities side by side, while a fraction such as 8⁄3 represents a single quantity split by another. This page is built around the fraction reading specifically, with fields labeled numerator and denominator rather than two generic ratio terms.
What does it mean if the GCF turns out to be 1?
It means the fraction is already in its lowest possible terms — the numerator and denominator share no common factor larger than 1, so dividing by the GCF changes nothing at all. Seven over five, for instance, cannot be reduced any further than 7⁄5 itself.
What if the GCF equals the denominator itself?
Then the simplified denominator becomes exactly 1, and the fraction reduces all the way to a whole number. One hundred over twenty-five, for example, has a GCF of 25, which is the denominator itself, so the fraction collapses to the whole number 4 over 1.