GCF of 812/349, 3738/870
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 812/349, 3738/870 i.e 14/303630 easily. The following is the detailed procedure to determine the greatest common factor of fractions 812/349, 3738/870.
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 812/349,3738/870?
Given fractions are 812/349,3738/870
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 812/349,3738/870, numerators are 812,3738
Denominators are 349,870
The GCF of 812,3738 is 14 .
LCM of 349,870 is 303630.
The greatest common factor of 812/349,3738/870 = [GCF of 812,3738]/[LCM of 349,870]= 14/303630
Therefore, the GCF of 812/349,3738/870 is 14/303630.
To find the highest common factor of 812,3738, we have to find the factors of both numbers and list the highest common factor.
The factors of 812 are 1, 2, 4, 7, 14, 28, 29, 58, 116, 203, 406, 812
The factors of 3738 are 1, 2, 3, 6, 7, 14, 21, 42, 89, 178, 267, 534, 623, 1246, 1869, 3738
The HCF of 812,3738 is 14.
Lets's calculate GCF of 812,3738
| 2 | 812, 3738 |
| 7 | 406, 1869 |
| 58, 267 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 812,3738 By Matching Biggest Common Factor Method
Now, list down the factors of 812
:1,2,4,7,14,28,29,58,116,203,406,812
Now, list down the factors of 3738
:1,2,3,6,7,14,21,42,89,178,267,534,623,1246,1869,3738
Greatest Common Factor
We found the factors 812,3738 . The biggest common factor number is the GCF number.
So the greatest common factor 812,3738 is 14.
Lets's calculate LCM of 349,870
Given numbers has no common factors except 1. So, there LCM is their product i.e 303630
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/303630
Therefore, the GCF of Fractions 812/349,3738/870 is 14/303630
Least Common Multiple of 349,870 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 349,870 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(349,870) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(349,870) x common factors =1 x 1 = 1
LCM(349,870) = ( 349 × 870 ) / 1
LCM(349,870) = 303630 / 1
LCM(349,870) = 303630
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FAQs on GCF of Fractions of 812/349, 3738/870
1. What is the HCF of 812,3738?
The HCF of 812,3738 is 14
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 812/349, 3738/870?
Answer: GCF of Numerators as per given numbers 812/349, 3738/870 is
GCF of Numerators i.e. for 812,3738 is 14
LCM of denominators i.e. for 349,870 is 303630.
Thus, GCF of Fractions is 14/303630.Finally, GCF of Fractions for 812/349, 3738/870 is 14/303630.