GCF of 978/174, 2664/257
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 978/174, 2664/257 i.e 6/44718 easily. The following is the detailed procedure to determine the greatest common factor of fractions 978/174, 2664/257.
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 978/174,2664/257?
Given fractions are 978/174,2664/257
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 978/174,2664/257, numerators are 978,2664
Denominators are 174,257
The GCF of 978,2664 is 6 .
LCM of 174,257 is 44718.
The greatest common factor of 978/174,2664/257 = [GCF of 978,2664]/[LCM of 174,257]= 6/44718
Therefore, the GCF of 978/174,2664/257 is 6/44718.
To find the highest common factor of 978,2664, we have to find the factors of both numbers and list the highest common factor.
The factors of 978 are 1, 2, 3, 6, 163, 326, 489, 978
The factors of 2664 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 37, 72, 74, 111, 148, 222, 296, 333, 444, 666, 888, 1332, 2664
The HCF of 978,2664 is 6.
Lets's calculate GCF of 978,2664
| 2 | 978, 2664 |
| 3 | 489, 1332 |
| 163, 444 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 978,2664 By Matching Biggest Common Factor Method
Now, list down the factors of 978
:1,2,3,6,163,326,489,978
Now, list down the factors of 2664
:1,2,3,4,6,8,9,12,18,24,36,37,72,74,111,148,222,296,333,444,666,888,1332,2664
Greatest Common Factor
We found the factors 978,2664 . The biggest common factor number is the GCF number.
So the greatest common factor 978,2664 is 6.
Lets's calculate LCM of 174,257
Given numbers has no common factors except 1. So, there LCM is their product i.e 44718
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/44718
Therefore, the GCF of Fractions 978/174,2664/257 is 6/44718
Least Common Multiple of 174,257 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 174,257 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(174,257) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(174,257) x common factors =1 x 1 = 1
LCM(174,257) = ( 174 × 257 ) / 1
LCM(174,257) = 44718 / 1
LCM(174,257) = 44718
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FAQs on GCF of Fractions of 978/174, 2664/257
1. What is the HCF of 978,2664?
The HCF of 978,2664 is 6
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 978/174, 2664/257?
Answer: GCF of Numerators as per given numbers 978/174, 2664/257 is
GCF of Numerators i.e. for 978,2664 is 6
LCM of denominators i.e. for 174,257 is 44718.
Thus, GCF of Fractions is 6/44718.Finally, GCF of Fractions for 978/174, 2664/257 is 6/44718.