GCF of 653/82, 746/84, 418/22
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 653/82, 746/84, 418/22 i.e 1/37884 easily. The following is the detailed procedure to determine the greatest common factor of fractions 653/82, 746/84, 418/22.
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 653/82,746/84,418/22?
Given fractions are 653/82,746/84,418/22
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 653/82,746/84,418/22, numerators are 653,746,418
Denominators are 82,84,22
The GCF of 653,746,418 is 1 .
LCM of 82,84,22 is 37884.
The greatest common factor of 653/82,746/84,418/22 = [GCF of 653,746,418]/[LCM of 82,84,22]= 1/37884
Therefore, the GCF of 653/82,746/84,418/22 is 1/37884.
To find the highest common factor of 653,746,418, we have to find the factors of both numbers and list the highest common factor.
The factors of 653 are 1, 653
The factors of 746 are 1, 2, 373, 746
The factors of 418 are 1, 2, 11, 19, 22, 38, 209, 418
The HCF of 653,746,418 is 1.
Lets's calculate GCF of 653,746,418
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 653,746,418 By Matching Biggest Common Factor Method
Now, list down the factors of 653
:1,653
Now, list down the factors of 746
:1,2,373,746
Now, list down the factors of 418
:1,2,11,19,22,38,209,418
Greatest Common Factor
We found the factors 653,746,418 . The biggest common factor number is the GCF number.
So the greatest common factor 653,746,418 is 1.
Lets's calculate LCM of 82,84,22
| 2 | 82, 84, 22 |
| 41, 42, 11 |
∴ So the LCM of the given numbers is 2 x 41 x 42 x 11 = 37884
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/37884
Therefore, the GCF of Fractions 653/82,746/84,418/22 is 1/37884
Least Common Multiple of 82,84,22 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 82,84,22 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(82,84,22) = 2
common factors(in case of two or more numbers have common factors) = 2
GCF(82,84,22) x common factors =2 x 2 = 4
LCM(82,84,22) = ( 82 × 84 × 22 ) / 4
LCM(82,84,22) = 151536 / 4
LCM(82,84,22) = 37884
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FAQs on GCF of Fractions of 653/82, 746/84, 418/22
1. What is the HCF of 653,746,418?
The HCF of 653,746,418 is 1
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 653/82, 746/84, 418/22?
Answer: GCF of Numerators as per given numbers 653/82, 746/84, 418/22 is
GCF of Numerators i.e. for 653,746,418 is 1
LCM of denominators i.e. for 82,84,22 is 37884.
Thus, GCF of Fractions is 1/37884.Finally, GCF of Fractions for 653/82, 746/84, 418/22 is 1/37884.