GCF of 5376/749, 2814/7186
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5376/749, 2814/7186 i.e 42/5382314 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5376/749, 2814/7186.
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 5376/749,2814/7186?
Given fractions are 5376/749,2814/7186
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 5376/749,2814/7186, numerators are 5376,2814
Denominators are 749,7186
The GCF of 5376,2814 is 42 .
LCM of 749,7186 is 5382314.
The greatest common factor of 5376/749,2814/7186 = [GCF of 5376,2814]/[LCM of 749,7186]= 42/5382314
Therefore, the GCF of 5376/749,2814/7186 is 42/5382314.
To find the highest common factor of 5376,2814, we have to find the factors of both numbers and list the highest common factor.
The factors of 5376 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 64, 84, 96, 112, 128, 168, 192, 224, 256, 336, 384, 448, 672, 768, 896, 1344, 1792, 2688, 5376
The factors of 2814 are 1, 2, 3, 6, 7, 14, 21, 42, 67, 134, 201, 402, 469, 938, 1407, 2814
The HCF of 5376,2814 is 42.
Lets's calculate GCF of 5376,2814
| 2 | 5376, 2814 |
| 3 | 2688, 1407 |
| 7 | 896, 469 |
| 128, 67 |
∴ So the GCF of the given numbers is 2 x 3 x 7 = 42
Greatest Common Factor of 5376,2814 By Matching Biggest Common Factor Method
Now, list down the factors of 5376
:1,2,3,4,6,7,8,12,14,16,21,24,28,32,42,48,56,64,84,96,112,128,168,192,224,256,336,384,448,672,768,896,1344,1792,2688,5376
Now, list down the factors of 2814
:1,2,3,6,7,14,21,42,67,134,201,402,469,938,1407,2814
Greatest Common Factor
We found the factors 5376,2814 . The biggest common factor number is the GCF number.
So the greatest common factor 5376,2814 is 42.
Lets's calculate LCM of 749,7186
Given numbers has no common factors except 1. So, there LCM is their product i.e 5382314
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 42/5382314
Therefore, the GCF of Fractions 5376/749,2814/7186 is 42/5382314
Least Common Multiple of 749,7186 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 749,7186 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(749,7186) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(749,7186) x common factors =1 x 1 = 1
LCM(749,7186) = ( 749 × 7186 ) / 1
LCM(749,7186) = 5382314 / 1
LCM(749,7186) = 5382314
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FAQs on GCF of Fractions of 5376/749, 2814/7186
1. What is the HCF of 5376,2814?
The HCF of 5376,2814 is 42
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 5376/749, 2814/7186?
Answer: GCF of Numerators as per given numbers 5376/749, 2814/7186 is
GCF of Numerators i.e. for 5376,2814 is 42
LCM of denominators i.e. for 749,7186 is 5382314.
Thus, GCF of Fractions is 42/5382314.Finally, GCF of Fractions for 5376/749, 2814/7186 is 42/5382314.