GCF of 413/72, 714/32, 314/76
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 413/72, 714/32, 314/76 i.e 1/5472 easily. The following is the detailed procedure to determine the greatest common factor of fractions 413/72, 714/32, 314/76.
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 413/72,714/32,314/76?
Given fractions are 413/72,714/32,314/76
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 413/72,714/32,314/76, numerators are 413,714,314
Denominators are 72,32,76
The GCF of 413,714,314 is 1 .
LCM of 72,32,76 is 5472.
The greatest common factor of 413/72,714/32,314/76 = [GCF of 413,714,314]/[LCM of 72,32,76]= 1/5472
Therefore, the GCF of 413/72,714/32,314/76 is 1/5472.
To find the highest common factor of 413,714,314, we have to find the factors of both numbers and list the highest common factor.
The factors of 413 are 1, 7, 59, 413
The factors of 714 are 1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 357, 714
The factors of 314 are 1, 2, 157, 314
The HCF of 413,714,314 is 1.
Lets's calculate GCF of 413,714,314
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 413,714,314 By Matching Biggest Common Factor Method
Now, list down the factors of 413
:1,7,59,413
Now, list down the factors of 714
:1,2,3,6,7,14,17,21,34,42,51,102,119,238,357,714
Now, list down the factors of 314
:1,2,157,314
Greatest Common Factor
We found the factors 413,714,314 . The biggest common factor number is the GCF number.
So the greatest common factor 413,714,314 is 1.
Lets's calculate LCM of 72,32,76
| 2 | 72, 32, 76 |
| 2 | 36, 16, 38 |
| 2 | 18, 8, 19 |
| 9, 4, 19 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 9 x 4 x 19 = 5472
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/5472
Therefore, the GCF of Fractions 413/72,714/32,314/76 is 1/5472
Least Common Multiple of 72,32,76 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 72,32,76 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(72,32,76) = 4
common factors(in case of two or more numbers have common factors) = 8
GCF(72,32,76) x common factors =4 x 8 = 32
LCM(72,32,76) = ( 72 × 32 × 76 ) / 32
LCM(72,32,76) = 175104 / 32
LCM(72,32,76) = 5472
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 413/72, 714/32, 314/76
1. What is the HCF of 413,714,314?
The HCF of 413,714,314 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 413/72, 714/32, 314/76?
Answer: GCF of Numerators as per given numbers 413/72, 714/32, 314/76 is
GCF of Numerators i.e. for 413,714,314 is 1
LCM of denominators i.e. for 72,32,76 is 5472.
Thus, GCF of Fractions is 1/5472.Finally, GCF of Fractions for 413/72, 714/32, 314/76 is 1/5472.