GCF of 9709/189, 7152/156
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 9709/189, 7152/156 i.e 1/9828 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9709/189, 7152/156.
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 9709/189,7152/156?
Given fractions are 9709/189,7152/156
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 9709/189,7152/156, numerators are 9709,7152
Denominators are 189,156
The GCF of 9709,7152 is 1 .
LCM of 189,156 is 9828.
The greatest common factor of 9709/189,7152/156 = [GCF of 9709,7152]/[LCM of 189,156]= 1/9828
Therefore, the GCF of 9709/189,7152/156 is 1/9828.
To find the highest common factor of 9709,7152, we have to find the factors of both numbers and list the highest common factor.
The factors of 9709 are 1, 7, 19, 73, 133, 511, 1387, 9709
The factors of 7152 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 149, 298, 447, 596, 894, 1192, 1788, 2384, 3576, 7152
The HCF of 9709,7152 is 1.
Lets's calculate GCF of 9709,7152
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 9709,7152 By Matching Biggest Common Factor Method
Now, list down the factors of 9709
:1,7,19,73,133,511,1387,9709
Now, list down the factors of 7152
:1,2,3,4,6,8,12,16,24,48,149,298,447,596,894,1192,1788,2384,3576,7152
Greatest Common Factor
We found the factors 9709,7152 . The biggest common factor number is the GCF number.
So the greatest common factor 9709,7152 is 1.
Lets's calculate LCM of 189,156
| 3 | 189, 156 |
| 63, 52 |
∴ So the LCM of the given numbers is 3 x 63 x 52 = 9828
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/9828
Therefore, the GCF of Fractions 9709/189,7152/156 is 1/9828
Least Common Multiple of 189,156 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 189,156 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(189,156) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(189,156) x common factors =3 x 1 = 3
LCM(189,156) = ( 189 × 156 ) / 3
LCM(189,156) = 29484 / 3
LCM(189,156) = 9828
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FAQs on GCF of Fractions of 9709/189, 7152/156
1. What is the HCF of 9709,7152?
The HCF of 9709,7152 is 1
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 9709/189, 7152/156?
Answer: GCF of Numerators as per given numbers 9709/189, 7152/156 is
GCF of Numerators i.e. for 9709,7152 is 1
LCM of denominators i.e. for 189,156 is 9828.
Thus, GCF of Fractions is 1/9828.Finally, GCF of Fractions for 9709/189, 7152/156 is 1/9828.