GCF of 646/774, 551/414
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 646/774, 551/414 i.e 19/17802 easily. The following is the detailed procedure to determine the greatest common factor of fractions 646/774, 551/414.
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 646/774,551/414?
Given fractions are 646/774,551/414
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 646/774,551/414, numerators are 646,551
Denominators are 774,414
The GCF of 646,551 is 19 .
LCM of 774,414 is 17802.
The greatest common factor of 646/774,551/414 = [GCF of 646,551]/[LCM of 774,414]= 19/17802
Therefore, the GCF of 646/774,551/414 is 19/17802.
To find the highest common factor of 646,551, we have to find the factors of both numbers and list the highest common factor.
The factors of 646 are 1, 2, 17, 19, 34, 38, 323, 646
The factors of 551 are 1, 19, 29, 551
The HCF of 646,551 is 19.
Lets's calculate GCF of 646,551
| 19 | 646, 551 |
| 34, 29 |
∴ So the GCF of the given numbers is 19 = 19
Greatest Common Factor of 646,551 By Matching Biggest Common Factor Method
Now, list down the factors of 646
:1,2,17,19,34,38,323,646
Now, list down the factors of 551
:1,19,29,551
Greatest Common Factor
We found the factors 646,551 . The biggest common factor number is the GCF number.
So the greatest common factor 646,551 is 19.
Lets's calculate LCM of 774,414
| 2 | 774, 414 |
| 3 | 387, 207 |
| 3 | 129, 69 |
| 43, 23 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 43 x 23 = 17802
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 19/17802
Therefore, the GCF of Fractions 646/774,551/414 is 19/17802
Least Common Multiple of 774,414 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 774,414 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(774,414) = 18
common factors(in case of two or more numbers have common factors) = 1
GCF(774,414) x common factors =18 x 1 = 18
LCM(774,414) = ( 774 × 414 ) / 18
LCM(774,414) = 320436 / 18
LCM(774,414) = 17802
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FAQs on GCF of Fractions of 646/774, 551/414
1. What is the HCF of 646,551?
The HCF of 646,551 is 19
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 646/774, 551/414?
Answer: GCF of Numerators as per given numbers 646/774, 551/414 is
GCF of Numerators i.e. for 646,551 is 19
LCM of denominators i.e. for 774,414 is 17802.
Thus, GCF of Fractions is 19/17802.Finally, GCF of Fractions for 646/774, 551/414 is 19/17802.