GCF of 637/209, 217/946
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 637/209, 217/946 i.e 7/17974 easily. The following is the detailed procedure to determine the greatest common factor of fractions 637/209, 217/946.
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 637/209,217/946?
Given fractions are 637/209,217/946
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 637/209,217/946, numerators are 637,217
Denominators are 209,946
The GCF of 637,217 is 7 .
LCM of 209,946 is 17974.
The greatest common factor of 637/209,217/946 = [GCF of 637,217]/[LCM of 209,946]= 7/17974
Therefore, the GCF of 637/209,217/946 is 7/17974.
To find the highest common factor of 637,217, we have to find the factors of both numbers and list the highest common factor.
The factors of 637 are 1, 7, 13, 49, 91, 637
The factors of 217 are 1, 7, 31, 217
The HCF of 637,217 is 7.
Lets's calculate GCF of 637,217
| 7 | 637, 217 |
| 91, 31 |
∴ So the GCF of the given numbers is 7 = 7
Greatest Common Factor of 637,217 By Matching Biggest Common Factor Method
Now, list down the factors of 637
:1,7,13,49,91,637
Now, list down the factors of 217
:1,7,31,217
Greatest Common Factor
We found the factors 637,217 . The biggest common factor number is the GCF number.
So the greatest common factor 637,217 is 7.
Lets's calculate LCM of 209,946
| 11 | 209, 946 |
| 19, 86 |
∴ So the LCM of the given numbers is 11 x 19 x 86 = 17974
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/17974
Therefore, the GCF of Fractions 637/209,217/946 is 7/17974
Least Common Multiple of 209,946 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 209,946 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(209,946) = 11
common factors(in case of two or more numbers have common factors) = 1
GCF(209,946) x common factors =11 x 1 = 11
LCM(209,946) = ( 209 × 946 ) / 11
LCM(209,946) = 197714 / 11
LCM(209,946) = 17974
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 637/209, 217/946
1. What is the HCF of 637,217?
The HCF of 637,217 is 7
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 637/209, 217/946?
Answer: GCF of Numerators as per given numbers 637/209, 217/946 is
GCF of Numerators i.e. for 637,217 is 7
LCM of denominators i.e. for 209,946 is 17974.
Thus, GCF of Fractions is 7/17974.Finally, GCF of Fractions for 637/209, 217/946 is 7/17974.