GCF of 152/378, 8512/8014
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 152/378, 8512/8014 i.e 152/1514646 easily. The following is the detailed procedure to determine the greatest common factor of fractions 152/378, 8512/8014.
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 152/378,8512/8014?
Given fractions are 152/378,8512/8014
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 152/378,8512/8014, numerators are 152,8512
Denominators are 378,8014
The GCF of 152,8512 is 152 .
LCM of 378,8014 is 1514646.
The greatest common factor of 152/378,8512/8014 = [GCF of 152,8512]/[LCM of 378,8014]= 152/1514646
Therefore, the GCF of 152/378,8512/8014 is 152/1514646.
To find the highest common factor of 152,8512, we have to find the factors of both numbers and list the highest common factor.
The factors of 152 are 1, 2, 4, 8, 19, 38, 76, 152
The factors of 8512 are 1, 2, 4, 7, 8, 14, 16, 19, 28, 32, 38, 56, 64, 76, 112, 133, 152, 224, 266, 304, 448, 532, 608, 1064, 1216, 2128, 4256, 8512
The HCF of 152,8512 is 152.
Lets's calculate GCF of 152,8512
| 2 | 152, 8512 |
| 2 | 76, 4256 |
| 2 | 38, 2128 |
| 19 | 19, 1064 |
| 1, 56 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 19 = 152
Greatest Common Factor of 152,8512 By Matching Biggest Common Factor Method
Now, list down the factors of 152
:1,2,4,8,19,38,76,152
Now, list down the factors of 8512
:1,2,4,7,8,14,16,19,28,32,38,56,64,76,112,133,152,224,266,304,448,532,608,1064,1216,2128,4256,8512
Greatest Common Factor
We found the factors 152,8512 . The biggest common factor number is the GCF number.
So the greatest common factor 152,8512 is 152.
Lets's calculate LCM of 378,8014
| 2 | 378, 8014 |
| 189, 4007 |
∴ So the LCM of the given numbers is 2 x 189 x 4007 = 1514646
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 152/1514646
Therefore, the GCF of Fractions 152/378,8512/8014 is 152/1514646
Least Common Multiple of 378,8014 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 378,8014 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(378,8014) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(378,8014) x common factors =2 x 1 = 2
LCM(378,8014) = ( 378 × 8014 ) / 2
LCM(378,8014) = 3029292 / 2
LCM(378,8014) = 1514646
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FAQs on GCF of Fractions of 152/378, 8512/8014
1. What is the HCF of 152,8512?
The HCF of 152,8512 is 152
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 152/378, 8512/8014?
Answer: GCF of Numerators as per given numbers 152/378, 8512/8014 is
GCF of Numerators i.e. for 152,8512 is 152
LCM of denominators i.e. for 378,8014 is 1514646.
Thus, GCF of Fractions is 152/1514646.Finally, GCF of Fractions for 152/378, 8512/8014 is 152/1514646.