GCF of 1418/420, 7766/7749
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1418/420, 7766/7749 i.e 2/154980 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1418/420, 7766/7749.
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 1418/420,7766/7749?
Given fractions are 1418/420,7766/7749
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 1418/420,7766/7749, numerators are 1418,7766
Denominators are 420,7749
The GCF of 1418,7766 is 2 .
LCM of 420,7749 is 154980.
The greatest common factor of 1418/420,7766/7749 = [GCF of 1418,7766]/[LCM of 420,7749]= 2/154980
Therefore, the GCF of 1418/420,7766/7749 is 2/154980.
To find the highest common factor of 1418,7766, we have to find the factors of both numbers and list the highest common factor.
The factors of 1418 are 1, 2, 709, 1418
The factors of 7766 are 1, 2, 11, 22, 353, 706, 3883, 7766
The HCF of 1418,7766 is 2.
Lets's calculate GCF of 1418,7766
| 2 | 1418, 7766 |
| 709, 3883 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 1418,7766 By Matching Biggest Common Factor Method
Now, list down the factors of 1418
:1,2,709,1418
Now, list down the factors of 7766
:1,2,11,22,353,706,3883,7766
Greatest Common Factor
We found the factors 1418,7766 . The biggest common factor number is the GCF number.
So the greatest common factor 1418,7766 is 2.
Lets's calculate LCM of 420,7749
| 3 | 420, 7749 |
| 7 | 140, 2583 |
| 20, 369 |
∴ So the LCM of the given numbers is 3 x 7 x 20 x 369 = 154980
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/154980
Therefore, the GCF of Fractions 1418/420,7766/7749 is 2/154980
Least Common Multiple of 420,7749 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 420,7749 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(420,7749) = 21
common factors(in case of two or more numbers have common factors) = 1
GCF(420,7749) x common factors =21 x 1 = 21
LCM(420,7749) = ( 420 × 7749 ) / 21
LCM(420,7749) = 3254580 / 21
LCM(420,7749) = 154980
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FAQs on GCF of Fractions of 1418/420, 7766/7749
1. What is the HCF of 1418,7766?
The HCF of 1418,7766 is 2
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 1418/420, 7766/7749?
Answer: GCF of Numerators as per given numbers 1418/420, 7766/7749 is
GCF of Numerators i.e. for 1418,7766 is 2
LCM of denominators i.e. for 420,7749 is 154980.
Thus, GCF of Fractions is 2/154980.Finally, GCF of Fractions for 1418/420, 7766/7749 is 2/154980.