GCF of 255/345, 7752/634
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 255/345, 7752/634 i.e 51/218730 easily. The following is the detailed procedure to determine the greatest common factor of fractions 255/345, 7752/634.
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 255/345,7752/634?
Given fractions are 255/345,7752/634
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 255/345,7752/634, numerators are 255,7752
Denominators are 345,634
The GCF of 255,7752 is 51 .
LCM of 345,634 is 218730.
The greatest common factor of 255/345,7752/634 = [GCF of 255,7752]/[LCM of 345,634]= 51/218730
Therefore, the GCF of 255/345,7752/634 is 51/218730.
To find the highest common factor of 255,7752, we have to find the factors of both numbers and list the highest common factor.
The factors of 255 are 1, 3, 5, 15, 17, 51, 85, 255
The factors of 7752 are 1, 2, 3, 4, 6, 8, 12, 17, 19, 24, 34, 38, 51, 57, 68, 76, 102, 114, 136, 152, 204, 228, 323, 408, 456, 646, 969, 1292, 1938, 2584, 3876, 7752
The HCF of 255,7752 is 51.
Lets's calculate GCF of 255,7752
| 3 | 255, 7752 |
| 17 | 85, 2584 |
| 5, 152 |
∴ So the GCF of the given numbers is 3 x 17 = 51
Greatest Common Factor of 255,7752 By Matching Biggest Common Factor Method
Now, list down the factors of 255
:1,3,5,15,17,51,85,255
Now, list down the factors of 7752
:1,2,3,4,6,8,12,17,19,24,34,38,51,57,68,76,102,114,136,152,204,228,323,408,456,646,969,1292,1938,2584,3876,7752
Greatest Common Factor
We found the factors 255,7752 . The biggest common factor number is the GCF number.
So the greatest common factor 255,7752 is 51.
Lets's calculate LCM of 345,634
Given numbers has no common factors except 1. So, there LCM is their product i.e 218730
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 51/218730
Therefore, the GCF of Fractions 255/345,7752/634 is 51/218730
Least Common Multiple of 345,634 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 345,634 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(345,634) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(345,634) x common factors =1 x 1 = 1
LCM(345,634) = ( 345 × 634 ) / 1
LCM(345,634) = 218730 / 1
LCM(345,634) = 218730
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FAQs on GCF of Fractions of 255/345, 7752/634
1. What is the HCF of 255,7752?
The HCF of 255,7752 is 51
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 255/345, 7752/634?
Answer: GCF of Numerators as per given numbers 255/345, 7752/634 is
GCF of Numerators i.e. for 255,7752 is 51
LCM of denominators i.e. for 345,634 is 218730.
Thus, GCF of Fractions is 51/218730.Finally, GCF of Fractions for 255/345, 7752/634 is 51/218730.