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Simplify fractions to lowest terms using GCF. Shows step-by-step process with prime factorization.
This is the fastest method - it simplifies in one step!
Problem: Simplify 24/36
Step 1: Find GCF of 24 and 36
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
GCF = 12
Step 2: Divide: 24÷12 = 2, 36÷12 = 3
Answer: 2/3
If you can't find the GCF easily, divide by common factors repeatedly:
Example: 24/36 → ÷2 → 12/18 → ÷2 → 6/9 → ÷3 → 2/3
Simplifying a fraction means reducing it to its lowest terms - where the numerator and denominator have no common factors except 1. For example, 4/8 simplifies to 1/2 because both 4 and 8 can be divided by 4. The simplified fraction represents the same value but with smaller numbers.
List all factors of both numbers and find the largest one they share. Alternatively, use the Euclidean algorithm: repeatedly divide the larger by the smaller and replace the larger with the remainder until you get 0. The last non-zero remainder is the GCF. For 48 and 18: 48÷18=2 R12, 18÷12=1 R6, 12÷6=2 R0, so GCF=6.
No, some fractions are already in lowest terms. If the numerator and denominator share no common factors except 1 (they are coprime), the fraction cannot be simplified further. For example, 3/7, 5/8, and 11/13 are already in simplest form.
You can still simplify improper fractions (where numerator > denominator) the same way - divide both by their GCF. For example, 18/12 simplifies to 3/2. You can then optionally convert to a mixed number: 3/2 = 1 1/2.
Use prime factorization! Break both numbers into prime factors, then cancel out matching factors. For example, 210/294: 210=2×3×5×7, 294=2×3×7×7. Cancel common factors (2, 3, 7): 5/7. This is especially helpful when you can't easily see the GCF.
Simplify as usual, keeping the negative sign. By convention, place the negative in front of the fraction or with the numerator, not the denominator. For example, 8/-12 simplifies to -2/3 or -(2/3), never 2/-3.