GCF of 684/419, 123/165
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 684/419, 123/165 i.e 3/69135 easily. The following is the detailed procedure to determine the greatest common factor of fractions 684/419, 123/165.
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 684/419,123/165?
Given fractions are 684/419,123/165
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 684/419,123/165, numerators are 684,123
Denominators are 419,165
The GCF of 684,123 is 3 .
LCM of 419,165 is 69135.
The greatest common factor of 684/419,123/165 = [GCF of 684,123]/[LCM of 419,165]= 3/69135
Therefore, the GCF of 684/419,123/165 is 3/69135.
To find the highest common factor of 684,123, we have to find the factors of both numbers and list the highest common factor.
The factors of 684 are 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684
The factors of 123 are 1, 3, 41, 123
The HCF of 684,123 is 3.
Lets's calculate GCF of 684,123
| 3 | 684, 123 |
| 228, 41 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 684,123 By Matching Biggest Common Factor Method
Now, list down the factors of 684
:1,2,3,4,6,9,12,18,19,36,38,57,76,114,171,228,342,684
Now, list down the factors of 123
:1,3,41,123
Greatest Common Factor
We found the factors 684,123 . The biggest common factor number is the GCF number.
So the greatest common factor 684,123 is 3.
Lets's calculate LCM of 419,165
Given numbers has no common factors except 1. So, there LCM is their product i.e 69135
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/69135
Therefore, the GCF of Fractions 684/419,123/165 is 3/69135
Least Common Multiple of 419,165 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 419,165 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(419,165) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(419,165) x common factors =1 x 1 = 1
LCM(419,165) = ( 419 × 165 ) / 1
LCM(419,165) = 69135 / 1
LCM(419,165) = 69135
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FAQs on GCF of Fractions of 684/419, 123/165
1. What is the HCF of 684,123?
The HCF of 684,123 is 3
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 684/419, 123/165?
Answer: GCF of Numerators as per given numbers 684/419, 123/165 is
GCF of Numerators i.e. for 684,123 is 3
LCM of denominators i.e. for 419,165 is 69135.
Thus, GCF of Fractions is 3/69135.Finally, GCF of Fractions for 684/419, 123/165 is 3/69135.