GCF of 407/624, 592/678
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 407/624, 592/678 i.e 37/70512 easily. The following is the detailed procedure to determine the greatest common factor of fractions 407/624, 592/678.
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 407/624,592/678?
Given fractions are 407/624,592/678
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 407/624,592/678, numerators are 407,592
Denominators are 624,678
The GCF of 407,592 is 37 .
LCM of 624,678 is 70512.
The greatest common factor of 407/624,592/678 = [GCF of 407,592]/[LCM of 624,678]= 37/70512
Therefore, the GCF of 407/624,592/678 is 37/70512.
To find the highest common factor of 407,592, we have to find the factors of both numbers and list the highest common factor.
The factors of 407 are 1, 11, 37, 407
The factors of 592 are 1, 2, 4, 8, 16, 37, 74, 148, 296, 592
The HCF of 407,592 is 37.
Lets's calculate GCF of 407,592
| 37 | 407, 592 |
| 11, 16 |
∴ So the GCF of the given numbers is 37 = 37
Greatest Common Factor of 407,592 By Matching Biggest Common Factor Method
Now, list down the factors of 407
:1,11,37,407
Now, list down the factors of 592
:1,2,4,8,16,37,74,148,296,592
Greatest Common Factor
We found the factors 407,592 . The biggest common factor number is the GCF number.
So the greatest common factor 407,592 is 37.
Lets's calculate LCM of 624,678
| 2 | 624, 678 |
| 3 | 312, 339 |
| 104, 113 |
∴ So the LCM of the given numbers is 2 x 3 x 104 x 113 = 70512
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 37/70512
Therefore, the GCF of Fractions 407/624,592/678 is 37/70512
Least Common Multiple of 624,678 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 624,678 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(624,678) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(624,678) x common factors =6 x 1 = 6
LCM(624,678) = ( 624 × 678 ) / 6
LCM(624,678) = 423072 / 6
LCM(624,678) = 70512
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FAQs on GCF of Fractions of 407/624, 592/678
1. What is the HCF of 407,592?
The HCF of 407,592 is 37
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 407/624, 592/678?
Answer: GCF of Numerators as per given numbers 407/624, 592/678 is
GCF of Numerators i.e. for 407,592 is 37
LCM of denominators i.e. for 624,678 is 70512.
Thus, GCF of Fractions is 37/70512.Finally, GCF of Fractions for 407/624, 592/678 is 37/70512.