GCF of 1214/752, 3431/7280
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1214/752, 3431/7280 i.e 1/342160 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1214/752, 3431/7280.
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 1214/752,3431/7280?
Given fractions are 1214/752,3431/7280
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 1214/752,3431/7280, numerators are 1214,3431
Denominators are 752,7280
The GCF of 1214,3431 is 1 .
LCM of 752,7280 is 342160.
The greatest common factor of 1214/752,3431/7280 = [GCF of 1214,3431]/[LCM of 752,7280]= 1/342160
Therefore, the GCF of 1214/752,3431/7280 is 1/342160.
To find the highest common factor of 1214,3431, we have to find the factors of both numbers and list the highest common factor.
The factors of 1214 are 1, 2, 607, 1214
The factors of 3431 are 1, 47, 73, 3431
The HCF of 1214,3431 is 1.
Lets's calculate GCF of 1214,3431
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 1214,3431 By Matching Biggest Common Factor Method
Now, list down the factors of 1214
:1,2,607,1214
Now, list down the factors of 3431
:1,47,73,3431
Greatest Common Factor
We found the factors 1214,3431 . The biggest common factor number is the GCF number.
So the greatest common factor 1214,3431 is 1.
Lets's calculate LCM of 752,7280
| 2 | 752, 7280 |
| 2 | 376, 3640 |
| 2 | 188, 1820 |
| 2 | 94, 910 |
| 47, 455 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 47 x 455 = 342160
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/342160
Therefore, the GCF of Fractions 1214/752,3431/7280 is 1/342160
Least Common Multiple of 752,7280 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 752,7280 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(752,7280) = 16
common factors(in case of two or more numbers have common factors) = 1
GCF(752,7280) x common factors =16 x 1 = 16
LCM(752,7280) = ( 752 × 7280 ) / 16
LCM(752,7280) = 5474560 / 16
LCM(752,7280) = 342160
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FAQs on GCF of Fractions of 1214/752, 3431/7280
1. What is the HCF of 1214,3431?
The HCF of 1214,3431 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 1214/752, 3431/7280?
Answer: GCF of Numerators as per given numbers 1214/752, 3431/7280 is
GCF of Numerators i.e. for 1214,3431 is 1
LCM of denominators i.e. for 752,7280 is 342160.
Thus, GCF of Fractions is 1/342160.Finally, GCF of Fractions for 1214/752, 3431/7280 is 1/342160.