GCF of 156/414, 7320/117
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 156/414, 7320/117 i.e 12/5382 easily. The following is the detailed procedure to determine the greatest common factor of fractions 156/414, 7320/117.
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 156/414,7320/117?
Given fractions are 156/414,7320/117
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 156/414,7320/117, numerators are 156,7320
Denominators are 414,117
The GCF of 156,7320 is 12 .
LCM of 414,117 is 5382.
The greatest common factor of 156/414,7320/117 = [GCF of 156,7320]/[LCM of 414,117]= 12/5382
Therefore, the GCF of 156/414,7320/117 is 12/5382.
To find the highest common factor of 156,7320, we have to find the factors of both numbers and list the highest common factor.
The factors of 156 are 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156
The factors of 7320 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 61, 120, 122, 183, 244, 305, 366, 488, 610, 732, 915, 1220, 1464, 1830, 2440, 3660, 7320
The HCF of 156,7320 is 12.
Lets's calculate GCF of 156,7320
| 2 | 156, 7320 |
| 2 | 78, 3660 |
| 3 | 39, 1830 |
| 13, 610 |
∴ So the GCF of the given numbers is 2 x 2 x 3 = 12
Greatest Common Factor of 156,7320 By Matching Biggest Common Factor Method
Now, list down the factors of 156
:1,2,3,4,6,12,13,26,39,52,78,156
Now, list down the factors of 7320
:1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,61,120,122,183,244,305,366,488,610,732,915,1220,1464,1830,2440,3660,7320
Greatest Common Factor
We found the factors 156,7320 . The biggest common factor number is the GCF number.
So the greatest common factor 156,7320 is 12.
Lets's calculate LCM of 414,117
| 3 | 414, 117 |
| 3 | 138, 39 |
| 46, 13 |
∴ So the LCM of the given numbers is 3 x 3 x 46 x 13 = 5382
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/5382
Therefore, the GCF of Fractions 156/414,7320/117 is 12/5382
Least Common Multiple of 414,117 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 414,117 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(414,117) = 9
common factors(in case of two or more numbers have common factors) = 1
GCF(414,117) x common factors =9 x 1 = 9
LCM(414,117) = ( 414 × 117 ) / 9
LCM(414,117) = 48438 / 9
LCM(414,117) = 5382
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FAQs on GCF of Fractions of 156/414, 7320/117
1. What is the HCF of 156,7320?
The HCF of 156,7320 is 12
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 156/414, 7320/117?
Answer: GCF of Numerators as per given numbers 156/414, 7320/117 is
GCF of Numerators i.e. for 156,7320 is 12
LCM of denominators i.e. for 414,117 is 5382.
Thus, GCF of Fractions is 12/5382.Finally, GCF of Fractions for 156/414, 7320/117 is 12/5382.