GCF of 354/42, 1504/690
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 354/42, 1504/690 i.e 2/4830 easily. The following is the detailed procedure to determine the greatest common factor of fractions 354/42, 1504/690.
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 354/42,1504/690?
Given fractions are 354/42,1504/690
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 354/42,1504/690, numerators are 354,1504
Denominators are 42,690
The GCF of 354,1504 is 2 .
LCM of 42,690 is 4830.
The greatest common factor of 354/42,1504/690 = [GCF of 354,1504]/[LCM of 42,690]= 2/4830
Therefore, the GCF of 354/42,1504/690 is 2/4830.
To find the highest common factor of 354,1504, we have to find the factors of both numbers and list the highest common factor.
The factors of 354 are 1, 2, 3, 6, 59, 118, 177, 354
The factors of 1504 are 1, 2, 4, 8, 16, 32, 47, 94, 188, 376, 752, 1504
The HCF of 354,1504 is 2.
Lets's calculate GCF of 354,1504
| 2 | 354, 1504 |
| 177, 752 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 354,1504 By Matching Biggest Common Factor Method
Now, list down the factors of 354
:1,2,3,6,59,118,177,354
Now, list down the factors of 1504
:1,2,4,8,16,32,47,94,188,376,752,1504
Greatest Common Factor
We found the factors 354,1504 . The biggest common factor number is the GCF number.
So the greatest common factor 354,1504 is 2.
Lets's calculate LCM of 42,690
| 2 | 42, 690 |
| 3 | 21, 345 |
| 7, 115 |
∴ So the LCM of the given numbers is 2 x 3 x 7 x 115 = 4830
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/4830
Therefore, the GCF of Fractions 354/42,1504/690 is 2/4830
Least Common Multiple of 42,690 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 42,690 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(42,690) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(42,690) x common factors =6 x 1 = 6
LCM(42,690) = ( 42 × 690 ) / 6
LCM(42,690) = 28980 / 6
LCM(42,690) = 4830
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FAQs on GCF of Fractions of 354/42, 1504/690
1. What is the HCF of 354,1504?
The HCF of 354,1504 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 354/42, 1504/690?
Answer: GCF of Numerators as per given numbers 354/42, 1504/690 is
GCF of Numerators i.e. for 354,1504 is 2
LCM of denominators i.e. for 42,690 is 4830.
Thus, GCF of Fractions is 2/4830.Finally, GCF of Fractions for 354/42, 1504/690 is 2/4830.