GCF of 8428/549, 9114/1570
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8428/549, 9114/1570 i.e 98/861930 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8428/549, 9114/1570.
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 8428/549,9114/1570?
Given fractions are 8428/549,9114/1570
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 8428/549,9114/1570, numerators are 8428,9114
Denominators are 549,1570
The GCF of 8428,9114 is 98 .
LCM of 549,1570 is 861930.
The greatest common factor of 8428/549,9114/1570 = [GCF of 8428,9114]/[LCM of 549,1570]= 98/861930
Therefore, the GCF of 8428/549,9114/1570 is 98/861930.
To find the highest common factor of 8428,9114, we have to find the factors of both numbers and list the highest common factor.
The factors of 8428 are 1, 2, 4, 7, 14, 28, 43, 49, 86, 98, 172, 196, 301, 602, 1204, 2107, 4214, 8428
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 8428,9114 is 98.
Lets's calculate GCF of 8428,9114
| 2 | 8428, 9114 |
| 7 | 4214, 4557 |
| 7 | 602, 651 |
| 86, 93 |
∴ So the GCF of the given numbers is 2 x 7 x 7 = 98
Greatest Common Factor of 8428,9114 By Matching Biggest Common Factor Method
Now, list down the factors of 8428
:1,2,4,7,14,28,43,49,86,98,172,196,301,602,1204,2107,4214,8428
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 8428,9114 . The biggest common factor number is the GCF number.
So the greatest common factor 8428,9114 is 98.
Lets's calculate LCM of 549,1570
Given numbers has no common factors except 1. So, there LCM is their product i.e 861930
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 98/861930
Therefore, the GCF of Fractions 8428/549,9114/1570 is 98/861930
Least Common Multiple of 549,1570 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 549,1570 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(549,1570) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(549,1570) x common factors =1 x 1 = 1
LCM(549,1570) = ( 549 × 1570 ) / 1
LCM(549,1570) = 861930 / 1
LCM(549,1570) = 861930
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FAQs on GCF of Fractions of 8428/549, 9114/1570
1. What is the HCF of 8428,9114?
The HCF of 8428,9114 is 98
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 8428/549, 9114/1570?
Answer: GCF of Numerators as per given numbers 8428/549, 9114/1570 is
GCF of Numerators i.e. for 8428,9114 is 98
LCM of denominators i.e. for 549,1570 is 861930.
Thus, GCF of Fractions is 98/861930.Finally, GCF of Fractions for 8428/549, 9114/1570 is 98/861930.