GCF of 532/306, 126/162
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 532/306, 126/162 i.e 14/2754 easily. The following is the detailed procedure to determine the greatest common factor of fractions 532/306, 126/162.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 532/306,126/162?
Given fractions are 532/306,126/162
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 532/306,126/162, numerators are 532,126
Denominators are 306,162
The GCF of 532,126 is 14 .
LCM of 306,162 is 2754.
The greatest common factor of 532/306,126/162 = [GCF of 532,126]/[LCM of 306,162]= 14/2754
Therefore, the GCF of 532/306,126/162 is 14/2754.
To find the highest common factor of 532,126, we have to find the factors of both numbers and list the highest common factor.
The factors of 532 are 1, 2, 4, 7, 14, 19, 28, 38, 76, 133, 266, 532
The factors of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126
The HCF of 532,126 is 14.
Lets's calculate GCF of 532,126
| 2 | 532, 126 |
| 7 | 266, 63 |
| 38, 9 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 532,126 By Matching Biggest Common Factor Method
Now, list down the factors of 532
:1,2,4,7,14,19,28,38,76,133,266,532
Now, list down the factors of 126
:1,2,3,6,7,9,14,18,21,42,63,126
Greatest Common Factor
We found the factors 532,126 . The biggest common factor number is the GCF number.
So the greatest common factor 532,126 is 14.
Lets's calculate LCM of 306,162
| 2 | 306, 162 |
| 3 | 153, 81 |
| 3 | 51, 27 |
| 17, 9 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 17 x 9 = 2754
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/2754
Therefore, the GCF of Fractions 532/306,126/162 is 14/2754
Least Common Multiple of 306,162 with GCF Formula
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 306,162 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(306,162) = 18
common factors(in case of two or more numbers have common factors) = 1
GCF(306,162) x common factors =18 x 1 = 18
LCM(306,162) = ( 306 × 162 ) / 18
LCM(306,162) = 49572 / 18
LCM(306,162) = 2754
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FAQs on GCF of Fractions of 532/306, 126/162
1. What is the HCF of 532,126?
The HCF of 532,126 is 14
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 532/306, 126/162?
Answer: GCF of Numerators as per given numbers 532/306, 126/162 is
GCF of Numerators i.e. for 532,126 is 14
LCM of denominators i.e. for 306,162 is 2754.
Thus, GCF of Fractions is 14/2754.Finally, GCF of Fractions for 532/306, 126/162 is 14/2754.