GCF of 693/42, 177/416
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 693/42, 177/416 i.e 3/8736 easily. The following is the detailed procedure to determine the greatest common factor of fractions 693/42, 177/416.
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 693/42,177/416?
Given fractions are 693/42,177/416
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 693/42,177/416, numerators are 693,177
Denominators are 42,416
The GCF of 693,177 is 3 .
LCM of 42,416 is 8736.
The greatest common factor of 693/42,177/416 = [GCF of 693,177]/[LCM of 42,416]= 3/8736
Therefore, the GCF of 693/42,177/416 is 3/8736.
To find the highest common factor of 693,177, we have to find the factors of both numbers and list the highest common factor.
The factors of 693 are 1, 3, 7, 9, 11, 21, 33, 63, 77, 99, 231, 693
The factors of 177 are 1, 3, 59, 177
The HCF of 693,177 is 3.
Lets's calculate GCF of 693,177
| 3 | 693, 177 |
| 231, 59 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 693,177 By Matching Biggest Common Factor Method
Now, list down the factors of 693
:1,3,7,9,11,21,33,63,77,99,231,693
Now, list down the factors of 177
:1,3,59,177
Greatest Common Factor
We found the factors 693,177 . The biggest common factor number is the GCF number.
So the greatest common factor 693,177 is 3.
Lets's calculate LCM of 42,416
| 2 | 42, 416 |
| 21, 208 |
∴ So the LCM of the given numbers is 2 x 21 x 208 = 8736
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/8736
Therefore, the GCF of Fractions 693/42,177/416 is 3/8736
Least Common Multiple of 42,416 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 42,416 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(42,416) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(42,416) x common factors =2 x 1 = 2
LCM(42,416) = ( 42 × 416 ) / 2
LCM(42,416) = 17472 / 2
LCM(42,416) = 8736
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FAQs on GCF of Fractions of 693/42, 177/416
1. What is the HCF of 693,177?
The HCF of 693,177 is 3
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 693/42, 177/416?
Answer: GCF of Numerators as per given numbers 693/42, 177/416 is
GCF of Numerators i.e. for 693,177 is 3
LCM of denominators i.e. for 42,416 is 8736.
Thus, GCF of Fractions is 3/8736.Finally, GCF of Fractions for 693/42, 177/416 is 3/8736.