GCF of 574/414, 688/633
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 574/414, 688/633 i.e 2/87354 easily. The following is the detailed procedure to determine the greatest common factor of fractions 574/414, 688/633.
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 574/414,688/633?
Given fractions are 574/414,688/633
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 574/414,688/633, numerators are 574,688
Denominators are 414,633
The GCF of 574,688 is 2 .
LCM of 414,633 is 87354.
The greatest common factor of 574/414,688/633 = [GCF of 574,688]/[LCM of 414,633]= 2/87354
Therefore, the GCF of 574/414,688/633 is 2/87354.
To find the highest common factor of 574,688, we have to find the factors of both numbers and list the highest common factor.
The factors of 574 are 1, 2, 7, 14, 41, 82, 287, 574
The factors of 688 are 1, 2, 4, 8, 16, 43, 86, 172, 344, 688
The HCF of 574,688 is 2.
Lets's calculate GCF of 574,688
| 2 | 574, 688 |
| 287, 344 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 574,688 By Matching Biggest Common Factor Method
Now, list down the factors of 574
:1,2,7,14,41,82,287,574
Now, list down the factors of 688
:1,2,4,8,16,43,86,172,344,688
Greatest Common Factor
We found the factors 574,688 . The biggest common factor number is the GCF number.
So the greatest common factor 574,688 is 2.
Lets's calculate LCM of 414,633
| 3 | 414, 633 |
| 138, 211 |
∴ So the LCM of the given numbers is 3 x 138 x 211 = 87354
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/87354
Therefore, the GCF of Fractions 574/414,688/633 is 2/87354
Least Common Multiple of 414,633 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 414,633 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(414,633) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(414,633) x common factors =3 x 1 = 3
LCM(414,633) = ( 414 × 633 ) / 3
LCM(414,633) = 262062 / 3
LCM(414,633) = 87354
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FAQs on GCF of Fractions of 574/414, 688/633
1. What is the HCF of 574,688?
The HCF of 574,688 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 574/414, 688/633?
Answer: GCF of Numerators as per given numbers 574/414, 688/633 is
GCF of Numerators i.e. for 574,688 is 2
LCM of denominators i.e. for 414,633 is 87354.
Thus, GCF of Fractions is 2/87354.Finally, GCF of Fractions for 574/414, 688/633 is 2/87354.