What Is 84/126 in Simplest Form?
84/126 simplified is 2/3. Divide the top and the bottom by the same number, their greatest common factor, and the value of the fraction stays the same.
Step 1: Find the GCF of 84 and 126
List the factors of each number and pick the biggest one they share.
- Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
- Factors of 126: 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126
- Common factors: 1, 2, 3, 6, 7, 14, 21, 42
The biggest common factor is 42, so GCF(84, 126) = 42.
Step 2: Divide the Top and Bottom by the GCF
84 ÷ 42 = 2 and 126 ÷ 42 = 3, so:
84/126 = 2/3
Another Way: Cancel the Shared Primes
- 84 = 2² × 3 × 7
- 126 = 2 × 3² × 7
Cancel the shared primes, 2 × 3 × 7, from the top and bottom. What is left is 2 on top and 3 on the bottom: 2/3.
Check the Answer
2 and 3 have no common factor except 1, so 2/3 is fully simplified. Both fractions equal about 0.6667 as a decimal.
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