GCF of 7656/123, 1414/8449
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7656/123, 1414/8449 i.e 2/1039227 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7656/123, 1414/8449.
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 7656/123,1414/8449?
Given fractions are 7656/123,1414/8449
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 7656/123,1414/8449, numerators are 7656,1414
Denominators are 123,8449
The GCF of 7656,1414 is 2 .
LCM of 123,8449 is 1039227.
The greatest common factor of 7656/123,1414/8449 = [GCF of 7656,1414]/[LCM of 123,8449]= 2/1039227
Therefore, the GCF of 7656/123,1414/8449 is 2/1039227.
To find the highest common factor of 7656,1414, we have to find the factors of both numbers and list the highest common factor.
The factors of 7656 are 1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 29, 33, 44, 58, 66, 87, 88, 116, 132, 174, 232, 264, 319, 348, 638, 696, 957, 1276, 1914, 2552, 3828, 7656
The factors of 1414 are 1, 2, 7, 14, 101, 202, 707, 1414
The HCF of 7656,1414 is 2.
Lets's calculate GCF of 7656,1414
| 2 | 7656, 1414 |
| 3828, 707 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 7656,1414 By Matching Biggest Common Factor Method
Now, list down the factors of 7656
:1,2,3,4,6,8,11,12,22,24,29,33,44,58,66,87,88,116,132,174,232,264,319,348,638,696,957,1276,1914,2552,3828,7656
Now, list down the factors of 1414
:1,2,7,14,101,202,707,1414
Greatest Common Factor
We found the factors 7656,1414 . The biggest common factor number is the GCF number.
So the greatest common factor 7656,1414 is 2.
Lets's calculate LCM of 123,8449
Given numbers has no common factors except 1. So, there LCM is their product i.e 1039227
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1039227
Therefore, the GCF of Fractions 7656/123,1414/8449 is 2/1039227
Least Common Multiple of 123,8449 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 123,8449 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(123,8449) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(123,8449) x common factors =1 x 1 = 1
LCM(123,8449) = ( 123 × 8449 ) / 1
LCM(123,8449) = 1039227 / 1
LCM(123,8449) = 1039227
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FAQs on GCF of Fractions of 7656/123, 1414/8449
1. What is the HCF of 7656,1414?
The HCF of 7656,1414 is 2
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 7656/123, 1414/8449?
Answer: GCF of Numerators as per given numbers 7656/123, 1414/8449 is
GCF of Numerators i.e. for 7656,1414 is 2
LCM of denominators i.e. for 123,8449 is 1039227.
Thus, GCF of Fractions is 2/1039227.Finally, GCF of Fractions for 7656/123, 1414/8449 is 2/1039227.