GCF of 354/77, 705/665
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 354/77, 705/665 i.e 3/7315 easily. The following is the detailed procedure to determine the greatest common factor of fractions 354/77, 705/665.
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 354/77,705/665?
Given fractions are 354/77,705/665
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 354/77,705/665, numerators are 354,705
Denominators are 77,665
The GCF of 354,705 is 3 .
LCM of 77,665 is 7315.
The greatest common factor of 354/77,705/665 = [GCF of 354,705]/[LCM of 77,665]= 3/7315
Therefore, the GCF of 354/77,705/665 is 3/7315.
To find the highest common factor of 354,705, we have to find the factors of both numbers and list the highest common factor.
The factors of 354 are 1, 2, 3, 6, 59, 118, 177, 354
The factors of 705 are 1, 3, 5, 15, 47, 141, 235, 705
The HCF of 354,705 is 3.
Lets's calculate GCF of 354,705
| 3 | 354, 705 |
| 118, 235 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 354,705 By Matching Biggest Common Factor Method
Now, list down the factors of 354
:1,2,3,6,59,118,177,354
Now, list down the factors of 705
:1,3,5,15,47,141,235,705
Greatest Common Factor
We found the factors 354,705 . The biggest common factor number is the GCF number.
So the greatest common factor 354,705 is 3.
Lets's calculate LCM of 77,665
| 7 | 77, 665 |
| 11, 95 |
∴ So the LCM of the given numbers is 7 x 11 x 95 = 7315
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/7315
Therefore, the GCF of Fractions 354/77,705/665 is 3/7315
Least Common Multiple of 77,665 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 77,665 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(77,665) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(77,665) x common factors =7 x 1 = 7
LCM(77,665) = ( 77 × 665 ) / 7
LCM(77,665) = 51205 / 7
LCM(77,665) = 7315
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FAQs on GCF of Fractions of 354/77, 705/665
1. What is the HCF of 354,705?
The HCF of 354,705 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 354/77, 705/665?
Answer: GCF of Numerators as per given numbers 354/77, 705/665 is
GCF of Numerators i.e. for 354,705 is 3
LCM of denominators i.e. for 77,665 is 7315.
Thus, GCF of Fractions is 3/7315.Finally, GCF of Fractions for 354/77, 705/665 is 3/7315.