GCF of 9712/156, 6512/1944
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 9712/156, 6512/1944 i.e 16/25272 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9712/156, 6512/1944.
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 9712/156,6512/1944?
Given fractions are 9712/156,6512/1944
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 9712/156,6512/1944, numerators are 9712,6512
Denominators are 156,1944
The GCF of 9712,6512 is 16 .
LCM of 156,1944 is 25272.
The greatest common factor of 9712/156,6512/1944 = [GCF of 9712,6512]/[LCM of 156,1944]= 16/25272
Therefore, the GCF of 9712/156,6512/1944 is 16/25272.
To find the highest common factor of 9712,6512, we have to find the factors of both numbers and list the highest common factor.
The factors of 9712 are 1, 2, 4, 8, 16, 607, 1214, 2428, 4856, 9712
The factors of 6512 are 1, 2, 4, 8, 11, 16, 22, 37, 44, 74, 88, 148, 176, 296, 407, 592, 814, 1628, 3256, 6512
The HCF of 9712,6512 is 16.
Lets's calculate GCF of 9712,6512
| 2 | 9712, 6512 |
| 2 | 4856, 3256 |
| 2 | 2428, 1628 |
| 2 | 1214, 814 |
| 607, 407 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 = 16
Greatest Common Factor of 9712,6512 By Matching Biggest Common Factor Method
Now, list down the factors of 9712
:1,2,4,8,16,607,1214,2428,4856,9712
Now, list down the factors of 6512
:1,2,4,8,11,16,22,37,44,74,88,148,176,296,407,592,814,1628,3256,6512
Greatest Common Factor
We found the factors 9712,6512 . The biggest common factor number is the GCF number.
So the greatest common factor 9712,6512 is 16.
Lets's calculate LCM of 156,1944
| 2 | 156, 1944 |
| 2 | 78, 972 |
| 3 | 39, 486 |
| 13, 162 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 13 x 162 = 25272
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 16/25272
Therefore, the GCF of Fractions 9712/156,6512/1944 is 16/25272
Least Common Multiple of 156,1944 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 156,1944 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(156,1944) = 12
common factors(in case of two or more numbers have common factors) = 1
GCF(156,1944) x common factors =12 x 1 = 12
LCM(156,1944) = ( 156 × 1944 ) / 12
LCM(156,1944) = 303264 / 12
LCM(156,1944) = 25272
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FAQs on GCF of Fractions of 9712/156, 6512/1944
1. What is the HCF of 9712,6512?
The HCF of 9712,6512 is 16
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 9712/156, 6512/1944?
Answer: GCF of Numerators as per given numbers 9712/156, 6512/1944 is
GCF of Numerators i.e. for 9712,6512 is 16
LCM of denominators i.e. for 156,1944 is 25272.
Thus, GCF of Fractions is 16/25272.Finally, GCF of Fractions for 9712/156, 6512/1944 is 16/25272.