GCF of 715/582, 3432/314
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 715/582, 3432/314 i.e 143/91374 easily. The following is the detailed procedure to determine the greatest common factor of fractions 715/582, 3432/314.
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 715/582,3432/314?
Given fractions are 715/582,3432/314
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 715/582,3432/314, numerators are 715,3432
Denominators are 582,314
The GCF of 715,3432 is 143 .
LCM of 582,314 is 91374.
The greatest common factor of 715/582,3432/314 = [GCF of 715,3432]/[LCM of 582,314]= 143/91374
Therefore, the GCF of 715/582,3432/314 is 143/91374.
To find the highest common factor of 715,3432, we have to find the factors of both numbers and list the highest common factor.
The factors of 715 are 1, 5, 11, 13, 55, 65, 143, 715
The factors of 3432 are 1, 2, 3, 4, 6, 8, 11, 12, 13, 22, 24, 26, 33, 39, 44, 52, 66, 78, 88, 104, 132, 143, 156, 264, 286, 312, 429, 572, 858, 1144, 1716, 3432
The HCF of 715,3432 is 143.
Lets's calculate GCF of 715,3432
| 11 | 715, 3432 |
| 13 | 65, 312 |
| 5, 24 |
∴ So the GCF of the given numbers is 11 x 13 = 143
Greatest Common Factor of 715,3432 By Matching Biggest Common Factor Method
Now, list down the factors of 715
:1,5,11,13,55,65,143,715
Now, list down the factors of 3432
:1,2,3,4,6,8,11,12,13,22,24,26,33,39,44,52,66,78,88,104,132,143,156,264,286,312,429,572,858,1144,1716,3432
Greatest Common Factor
We found the factors 715,3432 . The biggest common factor number is the GCF number.
So the greatest common factor 715,3432 is 143.
Lets's calculate LCM of 582,314
| 2 | 582, 314 |
| 291, 157 |
∴ So the LCM of the given numbers is 2 x 291 x 157 = 91374
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 143/91374
Therefore, the GCF of Fractions 715/582,3432/314 is 143/91374
Least Common Multiple of 582,314 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 582,314 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(582,314) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(582,314) x common factors =2 x 1 = 2
LCM(582,314) = ( 582 × 314 ) / 2
LCM(582,314) = 182748 / 2
LCM(582,314) = 91374
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FAQs on GCF of Fractions of 715/582, 3432/314
1. What is the HCF of 715,3432?
The HCF of 715,3432 is 143
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 715/582, 3432/314?
Answer: GCF of Numerators as per given numbers 715/582, 3432/314 is
GCF of Numerators i.e. for 715,3432 is 143
LCM of denominators i.e. for 582,314 is 91374.
Thus, GCF of Fractions is 143/91374.Finally, GCF of Fractions for 715/582, 3432/314 is 143/91374.