GCF of 8172/614, 5049/8676
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8172/614, 5049/8676 i.e 9/2663532 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8172/614, 5049/8676.
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 8172/614,5049/8676?
Given fractions are 8172/614,5049/8676
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 8172/614,5049/8676, numerators are 8172,5049
Denominators are 614,8676
The GCF of 8172,5049 is 9 .
LCM of 614,8676 is 2663532.
The greatest common factor of 8172/614,5049/8676 = [GCF of 8172,5049]/[LCM of 614,8676]= 9/2663532
Therefore, the GCF of 8172/614,5049/8676 is 9/2663532.
To find the highest common factor of 8172,5049, we have to find the factors of both numbers and list the highest common factor.
The factors of 8172 are 1, 2, 3, 4, 6, 9, 12, 18, 36, 227, 454, 681, 908, 1362, 2043, 2724, 4086, 8172
The factors of 5049 are 1, 3, 9, 11, 17, 27, 33, 51, 99, 153, 187, 297, 459, 561, 1683, 5049
The HCF of 8172,5049 is 9.
Lets's calculate GCF of 8172,5049
| 3 | 8172, 5049 |
| 3 | 2724, 1683 |
| 908, 561 |
∴ So the GCF of the given numbers is 3 x 3 = 9
Greatest Common Factor of 8172,5049 By Matching Biggest Common Factor Method
Now, list down the factors of 8172
:1,2,3,4,6,9,12,18,36,227,454,681,908,1362,2043,2724,4086,8172
Now, list down the factors of 5049
:1,3,9,11,17,27,33,51,99,153,187,297,459,561,1683,5049
Greatest Common Factor
We found the factors 8172,5049 . The biggest common factor number is the GCF number.
So the greatest common factor 8172,5049 is 9.
Lets's calculate LCM of 614,8676
| 2 | 614, 8676 |
| 307, 4338 |
∴ So the LCM of the given numbers is 2 x 307 x 4338 = 2663532
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 9/2663532
Therefore, the GCF of Fractions 8172/614,5049/8676 is 9/2663532
Least Common Multiple of 614,8676 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 614,8676 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(614,8676) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(614,8676) x common factors =2 x 1 = 2
LCM(614,8676) = ( 614 × 8676 ) / 2
LCM(614,8676) = 5327064 / 2
LCM(614,8676) = 2663532
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FAQs on GCF of Fractions of 8172/614, 5049/8676
1. What is the HCF of 8172,5049?
The HCF of 8172,5049 is 9
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 8172/614, 5049/8676?
Answer: GCF of Numerators as per given numbers 8172/614, 5049/8676 is
GCF of Numerators i.e. for 8172,5049 is 9
LCM of denominators i.e. for 614,8676 is 2663532.
Thus, GCF of Fractions is 9/2663532.Finally, GCF of Fractions for 8172/614, 5049/8676 is 9/2663532.