GCF of 872/420, 545/497
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 872/420, 545/497 i.e 109/29820 easily. The following is the detailed procedure to determine the greatest common factor of fractions 872/420, 545/497.
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 872/420,545/497?
Given fractions are 872/420,545/497
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 872/420,545/497, numerators are 872,545
Denominators are 420,497
The GCF of 872,545 is 109 .
LCM of 420,497 is 29820.
The greatest common factor of 872/420,545/497 = [GCF of 872,545]/[LCM of 420,497]= 109/29820
Therefore, the GCF of 872/420,545/497 is 109/29820.
To find the highest common factor of 872,545, we have to find the factors of both numbers and list the highest common factor.
The factors of 872 are 1, 2, 4, 8, 109, 218, 436, 872
The factors of 545 are 1, 5, 109, 545
The HCF of 872,545 is 109.
Lets's calculate GCF of 872,545
| 109 | 872, 545 |
| 8, 5 |
∴ So the GCF of the given numbers is 109 = 109
Greatest Common Factor of 872,545 By Matching Biggest Common Factor Method
Now, list down the factors of 872
:1,2,4,8,109,218,436,872
Now, list down the factors of 545
:1,5,109,545
Greatest Common Factor
We found the factors 872,545 . The biggest common factor number is the GCF number.
So the greatest common factor 872,545 is 109.
Lets's calculate LCM of 420,497
| 7 | 420, 497 |
| 60, 71 |
∴ So the LCM of the given numbers is 7 x 60 x 71 = 29820
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 109/29820
Therefore, the GCF of Fractions 872/420,545/497 is 109/29820
Least Common Multiple of 420,497 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 420,497 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(420,497) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(420,497) x common factors =7 x 1 = 7
LCM(420,497) = ( 420 × 497 ) / 7
LCM(420,497) = 208740 / 7
LCM(420,497) = 29820
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FAQs on GCF of Fractions of 872/420, 545/497
1. What is the HCF of 872,545?
The HCF of 872,545 is 109
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 872/420, 545/497?
Answer: GCF of Numerators as per given numbers 872/420, 545/497 is
GCF of Numerators i.e. for 872,545 is 109
LCM of denominators i.e. for 420,497 is 29820.
Thus, GCF of Fractions is 109/29820.Finally, GCF of Fractions for 872/420, 545/497 is 109/29820.