GCF of 7462/564, 9114/1917
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7462/564, 9114/1917 i.e 14/360396 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7462/564, 9114/1917.
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 7462/564,9114/1917?
Given fractions are 7462/564,9114/1917
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 7462/564,9114/1917, numerators are 7462,9114
Denominators are 564,1917
The GCF of 7462,9114 is 14 .
LCM of 564,1917 is 360396.
The greatest common factor of 7462/564,9114/1917 = [GCF of 7462,9114]/[LCM of 564,1917]= 14/360396
Therefore, the GCF of 7462/564,9114/1917 is 14/360396.
To find the highest common factor of 7462,9114, we have to find the factors of both numbers and list the highest common factor.
The factors of 7462 are 1, 2, 7, 13, 14, 26, 41, 82, 91, 182, 287, 533, 574, 1066, 3731, 7462
The factors of 9114 are 1, 2, 3, 6, 7, 14, 21, 31, 42, 49, 62, 93, 98, 147, 186, 217, 294, 434, 651, 1302, 1519, 3038, 4557, 9114
The HCF of 7462,9114 is 14.
Lets's calculate GCF of 7462,9114
| 2 | 7462, 9114 |
| 7 | 3731, 4557 |
| 533, 651 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 7462,9114 By Matching Biggest Common Factor Method
Now, list down the factors of 7462
:1,2,7,13,14,26,41,82,91,182,287,533,574,1066,3731,7462
Now, list down the factors of 9114
:1,2,3,6,7,14,21,31,42,49,62,93,98,147,186,217,294,434,651,1302,1519,3038,4557,9114
Greatest Common Factor
We found the factors 7462,9114 . The biggest common factor number is the GCF number.
So the greatest common factor 7462,9114 is 14.
Lets's calculate LCM of 564,1917
| 3 | 564, 1917 |
| 188, 639 |
∴ So the LCM of the given numbers is 3 x 188 x 639 = 360396
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/360396
Therefore, the GCF of Fractions 7462/564,9114/1917 is 14/360396
Least Common Multiple of 564,1917 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 564,1917 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(564,1917) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(564,1917) x common factors =3 x 1 = 3
LCM(564,1917) = ( 564 × 1917 ) / 3
LCM(564,1917) = 1081188 / 3
LCM(564,1917) = 360396
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FAQs on GCF of Fractions of 7462/564, 9114/1917
1. What is the HCF of 7462,9114?
The HCF of 7462,9114 is 14
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 7462/564, 9114/1917?
Answer: GCF of Numerators as per given numbers 7462/564, 9114/1917 is
GCF of Numerators i.e. for 7462,9114 is 14
LCM of denominators i.e. for 564,1917 is 360396.
Thus, GCF of Fractions is 14/360396.Finally, GCF of Fractions for 7462/564, 9114/1917 is 14/360396.