GCF of 698/678, 164/165
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 698/678, 164/165 i.e 2/37290 easily. The following is the detailed procedure to determine the greatest common factor of fractions 698/678, 164/165.
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 698/678,164/165?
Given fractions are 698/678,164/165
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 698/678,164/165, numerators are 698,164
Denominators are 678,165
The GCF of 698,164 is 2 .
LCM of 678,165 is 37290.
The greatest common factor of 698/678,164/165 = [GCF of 698,164]/[LCM of 678,165]= 2/37290
Therefore, the GCF of 698/678,164/165 is 2/37290.
To find the highest common factor of 698,164, we have to find the factors of both numbers and list the highest common factor.
The factors of 698 are 1, 2, 349, 698
The factors of 164 are 1, 2, 4, 41, 82, 164
The HCF of 698,164 is 2.
Lets's calculate GCF of 698,164
| 2 | 698, 164 |
| 349, 82 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 698,164 By Matching Biggest Common Factor Method
Now, list down the factors of 698
:1,2,349,698
Now, list down the factors of 164
:1,2,4,41,82,164
Greatest Common Factor
We found the factors 698,164 . The biggest common factor number is the GCF number.
So the greatest common factor 698,164 is 2.
Lets's calculate LCM of 678,165
| 3 | 678, 165 |
| 226, 55 |
∴ So the LCM of the given numbers is 3 x 226 x 55 = 37290
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/37290
Therefore, the GCF of Fractions 698/678,164/165 is 2/37290
Least Common Multiple of 678,165 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 678,165 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(678,165) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(678,165) x common factors =3 x 1 = 3
LCM(678,165) = ( 678 × 165 ) / 3
LCM(678,165) = 111870 / 3
LCM(678,165) = 37290
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FAQs on GCF of Fractions of 698/678, 164/165
1. What is the HCF of 698,164?
The HCF of 698,164 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 698/678, 164/165?
Answer: GCF of Numerators as per given numbers 698/678, 164/165 is
GCF of Numerators i.e. for 698,164 is 2
LCM of denominators i.e. for 678,165 is 37290.
Thus, GCF of Fractions is 2/37290.Finally, GCF of Fractions for 698/678, 164/165 is 2/37290.