GCF of 109/615, 705/624
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 109/615, 705/624 i.e 1/127920 easily. The following is the detailed procedure to determine the greatest common factor of fractions 109/615, 705/624.
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 109/615,705/624?
Given fractions are 109/615,705/624
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 109/615,705/624, numerators are 109,705
Denominators are 615,624
The GCF of 109,705 is 1 .
LCM of 615,624 is 127920.
The greatest common factor of 109/615,705/624 = [GCF of 109,705]/[LCM of 615,624]= 1/127920
Therefore, the GCF of 109/615,705/624 is 1/127920.
To find the highest common factor of 109,705, we have to find the factors of both numbers and list the highest common factor.
The factors of 109 are 1, 109
The factors of 705 are 1, 3, 5, 15, 47, 141, 235, 705
The HCF of 109,705 is 1.
Lets's calculate GCF of 109,705
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 109,705 By Matching Biggest Common Factor Method
Now, list down the factors of 109
:1,109
Now, list down the factors of 705
:1,3,5,15,47,141,235,705
Greatest Common Factor
We found the factors 109,705 . The biggest common factor number is the GCF number.
So the greatest common factor 109,705 is 1.
Lets's calculate LCM of 615,624
| 3 | 615, 624 |
| 205, 208 |
∴ So the LCM of the given numbers is 3 x 205 x 208 = 127920
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/127920
Therefore, the GCF of Fractions 109/615,705/624 is 1/127920
Least Common Multiple of 615,624 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 615,624 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(615,624) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(615,624) x common factors =3 x 1 = 3
LCM(615,624) = ( 615 × 624 ) / 3
LCM(615,624) = 383760 / 3
LCM(615,624) = 127920
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 109/615, 705/624
1. What is the HCF of 109,705?
The HCF of 109,705 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 109/615, 705/624?
Answer: GCF of Numerators as per given numbers 109/615, 705/624 is
GCF of Numerators i.e. for 109,705 is 1
LCM of denominators i.e. for 615,624 is 127920.
Thus, GCF of Fractions is 1/127920.Finally, GCF of Fractions for 109/615, 705/624 is 1/127920.