GCF of 1982/88, 2301/742
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1982/88, 2301/742 i.e 1/32648 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1982/88, 2301/742.
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 1982/88,2301/742?
Given fractions are 1982/88,2301/742
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 1982/88,2301/742, numerators are 1982,2301
Denominators are 88,742
The GCF of 1982,2301 is 1 .
LCM of 88,742 is 32648.
The greatest common factor of 1982/88,2301/742 = [GCF of 1982,2301]/[LCM of 88,742]= 1/32648
Therefore, the GCF of 1982/88,2301/742 is 1/32648.
To find the highest common factor of 1982,2301, we have to find the factors of both numbers and list the highest common factor.
The factors of 1982 are 1, 2, 991, 1982
The factors of 2301 are 1, 3, 13, 39, 59, 177, 767, 2301
The HCF of 1982,2301 is 1.
Lets's calculate GCF of 1982,2301
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 1982,2301 By Matching Biggest Common Factor Method
Now, list down the factors of 1982
:1,2,991,1982
Now, list down the factors of 2301
:1,3,13,39,59,177,767,2301
Greatest Common Factor
We found the factors 1982,2301 . The biggest common factor number is the GCF number.
So the greatest common factor 1982,2301 is 1.
Lets's calculate LCM of 88,742
| 2 | 88, 742 |
| 44, 371 |
∴ So the LCM of the given numbers is 2 x 44 x 371 = 32648
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/32648
Therefore, the GCF of Fractions 1982/88,2301/742 is 1/32648
Least Common Multiple of 88,742 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 88,742 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(88,742) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(88,742) x common factors =2 x 1 = 2
LCM(88,742) = ( 88 × 742 ) / 2
LCM(88,742) = 65296 / 2
LCM(88,742) = 32648
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FAQs on GCF of Fractions of 1982/88, 2301/742
1. What is the HCF of 1982,2301?
The HCF of 1982,2301 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 1982/88, 2301/742?
Answer: GCF of Numerators as per given numbers 1982/88, 2301/742 is
GCF of Numerators i.e. for 1982,2301 is 1
LCM of denominators i.e. for 88,742 is 32648.
Thus, GCF of Fractions is 1/32648.Finally, GCF of Fractions for 1982/88, 2301/742 is 1/32648.