GCF of 66/289, 312/626, 375/961
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 66/289, 312/626, 375/961 i.e 3/173858354 easily. The following is the detailed procedure to determine the greatest common factor of fractions 66/289, 312/626, 375/961.
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 66/289,312/626,375/961?
Given fractions are 66/289,312/626,375/961
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 66/289,312/626,375/961, numerators are 66,312,375
Denominators are 289,626,961
The GCF of 66,312,375 is 3 .
LCM of 289,626,961 is 173858354.
The greatest common factor of 66/289,312/626,375/961 = [GCF of 66,312,375]/[LCM of 289,626,961]= 3/173858354
Therefore, the GCF of 66/289,312/626,375/961 is 3/173858354.
To find the highest common factor of 66,312,375, we have to find the factors of both numbers and list the highest common factor.
The factors of 66 are 1, 2, 3, 6, 11, 22, 33, 66
The factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
The factors of 375 are 1, 3, 5, 15, 25, 75, 125, 375
The HCF of 66,312,375 is 3.
Lets's calculate GCF of 66,312,375
| 3 | 66, 312, 375 |
| 22, 104, 125 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 66,312,375 By Matching Biggest Common Factor Method
Now, list down the factors of 66
:1,2,3,6,11,22,33,66
Now, list down the factors of 312
:1,2,3,4,6,8,12,13,24,26,39,52,78,104,156,312
Now, list down the factors of 375
:1,3,5,15,25,75,125,375
Greatest Common Factor
We found the factors 66,312,375 . The biggest common factor number is the GCF number.
So the greatest common factor 66,312,375 is 3.
Lets's calculate LCM of 289,626,961
Given numbers has no common factors except 1. So, there LCM is their product i.e 173858354
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/173858354
Therefore, the GCF of Fractions 66/289,312/626,375/961 is 3/173858354
Least Common Multiple of 289,626,961 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 289,626,961 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(289,626,961) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(289,626,961) x common factors =1 x 1 = 1
LCM(289,626,961) = ( 289 × 626 × 961 ) / 1
LCM(289,626,961) = 173858354 / 1
LCM(289,626,961) = 173858354
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FAQs on GCF of Fractions of 66/289, 312/626, 375/961
1. What is the HCF of 66,312,375?
The HCF of 66,312,375 is 3
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 66/289, 312/626, 375/961?
Answer: GCF of Numerators as per given numbers 66/289, 312/626, 375/961 is
GCF of Numerators i.e. for 66,312,375 is 3
LCM of denominators i.e. for 289,626,961 is 173858354.
Thus, GCF of Fractions is 3/173858354.Finally, GCF of Fractions for 66/289, 312/626, 375/961 is 3/173858354.