GCF of 974/32, 140/7192
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 974/32, 140/7192 i.e 2/28768 easily. The following is the detailed procedure to determine the greatest common factor of fractions 974/32, 140/7192.
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 974/32,140/7192?
Given fractions are 974/32,140/7192
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 974/32,140/7192, numerators are 974,140
Denominators are 32,7192
The GCF of 974,140 is 2 .
LCM of 32,7192 is 28768.
The greatest common factor of 974/32,140/7192 = [GCF of 974,140]/[LCM of 32,7192]= 2/28768
Therefore, the GCF of 974/32,140/7192 is 2/28768.
To find the highest common factor of 974,140, we have to find the factors of both numbers and list the highest common factor.
The factors of 974 are 1, 2, 487, 974
The factors of 140 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140
The HCF of 974,140 is 2.
Lets's calculate GCF of 974,140
| 2 | 974, 140 |
| 487, 70 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 974,140 By Matching Biggest Common Factor Method
Now, list down the factors of 974
:1,2,487,974
Now, list down the factors of 140
:1,2,4,5,7,10,14,20,28,35,70,140
Greatest Common Factor
We found the factors 974,140 . The biggest common factor number is the GCF number.
So the greatest common factor 974,140 is 2.
Lets's calculate LCM of 32,7192
| 2 | 32, 7192 |
| 2 | 16, 3596 |
| 2 | 8, 1798 |
| 4, 899 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 4 x 899 = 28768
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/28768
Therefore, the GCF of Fractions 974/32,140/7192 is 2/28768
Least Common Multiple of 32,7192 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 32,7192 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(32,7192) = 8
common factors(in case of two or more numbers have common factors) = 1
GCF(32,7192) x common factors =8 x 1 = 8
LCM(32,7192) = ( 32 × 7192 ) / 8
LCM(32,7192) = 230144 / 8
LCM(32,7192) = 28768
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FAQs on GCF of Fractions of 974/32, 140/7192
1. What is the HCF of 974,140?
The HCF of 974,140 is 2
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 974/32, 140/7192?
Answer: GCF of Numerators as per given numbers 974/32, 140/7192 is
GCF of Numerators i.e. for 974,140 is 2
LCM of denominators i.e. for 32,7192 is 28768.
Thus, GCF of Fractions is 2/28768.Finally, GCF of Fractions for 974/32, 140/7192 is 2/28768.