GCF of 1406/14, 6346/382
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1406/14, 6346/382 i.e 38/2674 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1406/14, 6346/382.
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 1406/14,6346/382?
Given fractions are 1406/14,6346/382
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 1406/14,6346/382, numerators are 1406,6346
Denominators are 14,382
The GCF of 1406,6346 is 38 .
LCM of 14,382 is 2674.
The greatest common factor of 1406/14,6346/382 = [GCF of 1406,6346]/[LCM of 14,382]= 38/2674
Therefore, the GCF of 1406/14,6346/382 is 38/2674.
To find the highest common factor of 1406,6346, we have to find the factors of both numbers and list the highest common factor.
The factors of 1406 are 1, 2, 19, 37, 38, 74, 703, 1406
The factors of 6346 are 1, 2, 19, 38, 167, 334, 3173, 6346
The HCF of 1406,6346 is 38.
Lets's calculate GCF of 1406,6346
| 2 | 1406, 6346 |
| 19 | 703, 3173 |
| 37, 167 |
∴ So the GCF of the given numbers is 2 x 19 = 38
Greatest Common Factor of 1406,6346 By Matching Biggest Common Factor Method
Now, list down the factors of 1406
:1,2,19,37,38,74,703,1406
Now, list down the factors of 6346
:1,2,19,38,167,334,3173,6346
Greatest Common Factor
We found the factors 1406,6346 . The biggest common factor number is the GCF number.
So the greatest common factor 1406,6346 is 38.
Lets's calculate LCM of 14,382
| 2 | 14, 382 |
| 7, 191 |
∴ So the LCM of the given numbers is 2 x 7 x 191 = 2674
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 38/2674
Therefore, the GCF of Fractions 1406/14,6346/382 is 38/2674
Least Common Multiple of 14,382 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 14,382 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(14,382) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(14,382) x common factors =2 x 1 = 2
LCM(14,382) = ( 14 × 382 ) / 2
LCM(14,382) = 5348 / 2
LCM(14,382) = 2674
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FAQs on GCF of Fractions of 1406/14, 6346/382
1. What is the HCF of 1406,6346?
The HCF of 1406,6346 is 38
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 1406/14, 6346/382?
Answer: GCF of Numerators as per given numbers 1406/14, 6346/382 is
GCF of Numerators i.e. for 1406,6346 is 38
LCM of denominators i.e. for 14,382 is 2674.
Thus, GCF of Fractions is 38/2674.Finally, GCF of Fractions for 1406/14, 6346/382 is 38/2674.