GCF of 213/70, 923/7748
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 213/70, 923/7748 i.e 71/271180 easily. The following is the detailed procedure to determine the greatest common factor of fractions 213/70, 923/7748.
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 213/70,923/7748?
Given fractions are 213/70,923/7748
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 213/70,923/7748, numerators are 213,923
Denominators are 70,7748
The GCF of 213,923 is 71 .
LCM of 70,7748 is 271180.
The greatest common factor of 213/70,923/7748 = [GCF of 213,923]/[LCM of 70,7748]= 71/271180
Therefore, the GCF of 213/70,923/7748 is 71/271180.
To find the highest common factor of 213,923, we have to find the factors of both numbers and list the highest common factor.
The factors of 213 are 1, 3, 71, 213
The factors of 923 are 1, 13, 71, 923
The HCF of 213,923 is 71.
Lets's calculate GCF of 213,923
| 71 | 213, 923 |
| 3, 13 |
∴ So the GCF of the given numbers is 71 = 71
Greatest Common Factor of 213,923 By Matching Biggest Common Factor Method
Now, list down the factors of 213
:1,3,71,213
Now, list down the factors of 923
:1,13,71,923
Greatest Common Factor
We found the factors 213,923 . The biggest common factor number is the GCF number.
So the greatest common factor 213,923 is 71.
Lets's calculate LCM of 70,7748
| 2 | 70, 7748 |
| 35, 3874 |
∴ So the LCM of the given numbers is 2 x 35 x 3874 = 271180
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 71/271180
Therefore, the GCF of Fractions 213/70,923/7748 is 71/271180
Least Common Multiple of 70,7748 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 70,7748 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(70,7748) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(70,7748) x common factors =2 x 1 = 2
LCM(70,7748) = ( 70 × 7748 ) / 2
LCM(70,7748) = 542360 / 2
LCM(70,7748) = 271180
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FAQs on GCF of Fractions of 213/70, 923/7748
1. What is the HCF of 213,923?
The HCF of 213,923 is 71
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 213/70, 923/7748?
Answer: GCF of Numerators as per given numbers 213/70, 923/7748 is
GCF of Numerators i.e. for 213,923 is 71
LCM of denominators i.e. for 70,7748 is 271180.
Thus, GCF of Fractions is 71/271180.Finally, GCF of Fractions for 213/70, 923/7748 is 71/271180.