GCF of 7172/420, 8508/676
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7172/420, 8508/676 i.e 4/70980 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7172/420, 8508/676.
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 7172/420,8508/676?
Given fractions are 7172/420,8508/676
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 7172/420,8508/676, numerators are 7172,8508
Denominators are 420,676
The GCF of 7172,8508 is 4 .
LCM of 420,676 is 70980.
The greatest common factor of 7172/420,8508/676 = [GCF of 7172,8508]/[LCM of 420,676]= 4/70980
Therefore, the GCF of 7172/420,8508/676 is 4/70980.
To find the highest common factor of 7172,8508, we have to find the factors of both numbers and list the highest common factor.
The factors of 7172 are 1, 2, 4, 11, 22, 44, 163, 326, 652, 1793, 3586, 7172
The factors of 8508 are 1, 2, 3, 4, 6, 12, 709, 1418, 2127, 2836, 4254, 8508
The HCF of 7172,8508 is 4.
Lets's calculate GCF of 7172,8508
| 2 | 7172, 8508 |
| 2 | 3586, 4254 |
| 1793, 2127 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 7172,8508 By Matching Biggest Common Factor Method
Now, list down the factors of 7172
:1,2,4,11,22,44,163,326,652,1793,3586,7172
Now, list down the factors of 8508
:1,2,3,4,6,12,709,1418,2127,2836,4254,8508
Greatest Common Factor
We found the factors 7172,8508 . The biggest common factor number is the GCF number.
So the greatest common factor 7172,8508 is 4.
Lets's calculate LCM of 420,676
| 2 | 420, 676 |
| 2 | 210, 338 |
| 105, 169 |
∴ So the LCM of the given numbers is 2 x 2 x 105 x 169 = 70980
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/70980
Therefore, the GCF of Fractions 7172/420,8508/676 is 4/70980
Least Common Multiple of 420,676 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 420,676 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(420,676) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(420,676) x common factors =4 x 1 = 4
LCM(420,676) = ( 420 × 676 ) / 4
LCM(420,676) = 283920 / 4
LCM(420,676) = 70980
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FAQs on GCF of Fractions of 7172/420, 8508/676
1. What is the HCF of 7172,8508?
The HCF of 7172,8508 is 4
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 7172/420, 8508/676?
Answer: GCF of Numerators as per given numbers 7172/420, 8508/676 is
GCF of Numerators i.e. for 7172,8508 is 4
LCM of denominators i.e. for 420,676 is 70980.
Thus, GCF of Fractions is 4/70980.Finally, GCF of Fractions for 7172/420, 8508/676 is 4/70980.