GCF of 315/77, 769/748
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 315/77, 769/748 i.e 1/5236 easily. The following is the detailed procedure to determine the greatest common factor of fractions 315/77, 769/748.
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 315/77,769/748?
Given fractions are 315/77,769/748
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 315/77,769/748, numerators are 315,769
Denominators are 77,748
The GCF of 315,769 is 1 .
LCM of 77,748 is 5236.
The greatest common factor of 315/77,769/748 = [GCF of 315,769]/[LCM of 77,748]= 1/5236
Therefore, the GCF of 315/77,769/748 is 1/5236.
To find the highest common factor of 315,769, we have to find the factors of both numbers and list the highest common factor.
The factors of 315 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315
The factors of 769 are 1, 769
The HCF of 315,769 is 1.
Lets's calculate GCF of 315,769
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 315,769 By Matching Biggest Common Factor Method
Now, list down the factors of 315
:1,3,5,7,9,15,21,35,45,63,105,315
Now, list down the factors of 769
:1,769
Greatest Common Factor
We found the factors 315,769 . The biggest common factor number is the GCF number.
So the greatest common factor 315,769 is 1.
Lets's calculate LCM of 77,748
| 11 | 77, 748 |
| 7, 68 |
∴ So the LCM of the given numbers is 11 x 7 x 68 = 5236
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/5236
Therefore, the GCF of Fractions 315/77,769/748 is 1/5236
Least Common Multiple of 77,748 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 77,748 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(77,748) = 11
common factors(in case of two or more numbers have common factors) = 1
GCF(77,748) x common factors =11 x 1 = 11
LCM(77,748) = ( 77 × 748 ) / 11
LCM(77,748) = 57596 / 11
LCM(77,748) = 5236
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FAQs on GCF of Fractions of 315/77, 769/748
1. What is the HCF of 315,769?
The HCF of 315,769 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 315/77, 769/748?
Answer: GCF of Numerators as per given numbers 315/77, 769/748 is
GCF of Numerators i.e. for 315,769 is 1
LCM of denominators i.e. for 77,748 is 5236.
Thus, GCF of Fractions is 1/5236.Finally, GCF of Fractions for 315/77, 769/748 is 1/5236.