GCF of 700/348, 840/249
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 700/348, 840/249 i.e 140/28884 easily. The following is the detailed procedure to determine the greatest common factor of fractions 700/348, 840/249.
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 700/348,840/249?
Given fractions are 700/348,840/249
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 700/348,840/249, numerators are 700,840
Denominators are 348,249
The GCF of 700,840 is 140 .
LCM of 348,249 is 28884.
The greatest common factor of 700/348,840/249 = [GCF of 700,840]/[LCM of 348,249]= 140/28884
Therefore, the GCF of 700/348,840/249 is 140/28884.
To find the highest common factor of 700,840, we have to find the factors of both numbers and list the highest common factor.
The factors of 700 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, 350, 700
The factors of 840 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840
The HCF of 700,840 is 140.
Lets's calculate GCF of 700,840
| 2 | 700, 840 |
| 2 | 350, 420 |
| 5 | 175, 210 |
| 7 | 35, 42 |
| 5, 6 |
∴ So the GCF of the given numbers is 2 x 2 x 5 x 7 = 140
Greatest Common Factor of 700,840 By Matching Biggest Common Factor Method
Now, list down the factors of 700
:1,2,4,5,7,10,14,20,25,28,35,50,70,100,140,175,350,700
Now, list down the factors of 840
:1,2,3,4,5,6,7,8,10,12,14,15,20,21,24,28,30,35,40,42,56,60,70,84,105,120,140,168,210,280,420,840
Greatest Common Factor
We found the factors 700,840 . The biggest common factor number is the GCF number.
So the greatest common factor 700,840 is 140.
Lets's calculate LCM of 348,249
| 3 | 348, 249 |
| 116, 83 |
∴ So the LCM of the given numbers is 3 x 116 x 83 = 28884
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 140/28884
Therefore, the GCF of Fractions 700/348,840/249 is 140/28884
Least Common Multiple of 348,249 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 348,249 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(348,249) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(348,249) x common factors =3 x 1 = 3
LCM(348,249) = ( 348 × 249 ) / 3
LCM(348,249) = 86652 / 3
LCM(348,249) = 28884
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FAQs on GCF of Fractions of 700/348, 840/249
1. What is the HCF of 700,840?
The HCF of 700,840 is 140
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 700/348, 840/249?
Answer: GCF of Numerators as per given numbers 700/348, 840/249 is
GCF of Numerators i.e. for 700,840 is 140
LCM of denominators i.e. for 348,249 is 28884.
Thus, GCF of Fractions is 140/28884.Finally, GCF of Fractions for 700/348, 840/249 is 140/28884.