GCF of 7688/812, 3412/312
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7688/812, 3412/312 i.e 4/63336 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7688/812, 3412/312.
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 7688/812,3412/312?
Given fractions are 7688/812,3412/312
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 7688/812,3412/312, numerators are 7688,3412
Denominators are 812,312
The GCF of 7688,3412 is 4 .
LCM of 812,312 is 63336.
The greatest common factor of 7688/812,3412/312 = [GCF of 7688,3412]/[LCM of 812,312]= 4/63336
Therefore, the GCF of 7688/812,3412/312 is 4/63336.
To find the highest common factor of 7688,3412, we have to find the factors of both numbers and list the highest common factor.
The factors of 7688 are 1, 2, 4, 8, 31, 62, 124, 248, 961, 1922, 3844, 7688
The factors of 3412 are 1, 2, 4, 853, 1706, 3412
The HCF of 7688,3412 is 4.
Lets's calculate GCF of 7688,3412
| 2 | 7688, 3412 |
| 2 | 3844, 1706 |
| 1922, 853 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 7688,3412 By Matching Biggest Common Factor Method
Now, list down the factors of 7688
:1,2,4,8,31,62,124,248,961,1922,3844,7688
Now, list down the factors of 3412
:1,2,4,853,1706,3412
Greatest Common Factor
We found the factors 7688,3412 . The biggest common factor number is the GCF number.
So the greatest common factor 7688,3412 is 4.
Lets's calculate LCM of 812,312
| 2 | 812, 312 |
| 2 | 406, 156 |
| 203, 78 |
∴ So the LCM of the given numbers is 2 x 2 x 203 x 78 = 63336
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/63336
Therefore, the GCF of Fractions 7688/812,3412/312 is 4/63336
Least Common Multiple of 812,312 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 812,312 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(812,312) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(812,312) x common factors =4 x 1 = 4
LCM(812,312) = ( 812 × 312 ) / 4
LCM(812,312) = 253344 / 4
LCM(812,312) = 63336
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FAQs on GCF of Fractions of 7688/812, 3412/312
1. What is the HCF of 7688,3412?
The HCF of 7688,3412 is 4
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 7688/812, 3412/312?
Answer: GCF of Numerators as per given numbers 7688/812, 3412/312 is
GCF of Numerators i.e. for 7688,3412 is 4
LCM of denominators i.e. for 812,312 is 63336.
Thus, GCF of Fractions is 4/63336.Finally, GCF of Fractions for 7688/812, 3412/312 is 4/63336.