GCF of 810/76, 630/554
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 810/76, 630/554 i.e 90/21052 easily. The following is the detailed procedure to determine the greatest common factor of fractions 810/76, 630/554.
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 810/76,630/554?
Given fractions are 810/76,630/554
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 810/76,630/554, numerators are 810,630
Denominators are 76,554
The GCF of 810,630 is 90 .
LCM of 76,554 is 21052.
The greatest common factor of 810/76,630/554 = [GCF of 810,630]/[LCM of 76,554]= 90/21052
Therefore, the GCF of 810/76,630/554 is 90/21052.
To find the highest common factor of 810,630, we have to find the factors of both numbers and list the highest common factor.
The factors of 810 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405, 810
The factors of 630 are 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 63, 70, 90, 105, 126, 210, 315, 630
The HCF of 810,630 is 90.
Lets's calculate GCF of 810,630
| 2 | 810, 630 |
| 3 | 405, 315 |
| 3 | 135, 105 |
| 5 | 45, 35 |
| 9, 7 |
∴ So the GCF of the given numbers is 2 x 3 x 3 x 5 = 90
Greatest Common Factor of 810,630 By Matching Biggest Common Factor Method
Now, list down the factors of 810
:1,2,3,5,6,9,10,15,18,27,30,45,54,81,90,135,162,270,405,810
Now, list down the factors of 630
:1,2,3,5,6,7,9,10,14,15,18,21,30,35,42,45,63,70,90,105,126,210,315,630
Greatest Common Factor
We found the factors 810,630 . The biggest common factor number is the GCF number.
So the greatest common factor 810,630 is 90.
Lets's calculate LCM of 76,554
| 2 | 76, 554 |
| 38, 277 |
∴ So the LCM of the given numbers is 2 x 38 x 277 = 21052
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 90/21052
Therefore, the GCF of Fractions 810/76,630/554 is 90/21052
Least Common Multiple of 76,554 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 76,554 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(76,554) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(76,554) x common factors =2 x 1 = 2
LCM(76,554) = ( 76 × 554 ) / 2
LCM(76,554) = 42104 / 2
LCM(76,554) = 21052
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FAQs on GCF of Fractions of 810/76, 630/554
1. What is the HCF of 810,630?
The HCF of 810,630 is 90
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 810/76, 630/554?
Answer: GCF of Numerators as per given numbers 810/76, 630/554 is
GCF of Numerators i.e. for 810,630 is 90
LCM of denominators i.e. for 76,554 is 21052.
Thus, GCF of Fractions is 90/21052.Finally, GCF of Fractions for 810/76, 630/554 is 90/21052.