GCF of 697/28, 205/5314
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 697/28, 205/5314 i.e 41/74396 easily. The following is the detailed procedure to determine the greatest common factor of fractions 697/28, 205/5314.
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 697/28,205/5314?
Given fractions are 697/28,205/5314
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 697/28,205/5314, numerators are 697,205
Denominators are 28,5314
The GCF of 697,205 is 41 .
LCM of 28,5314 is 74396.
The greatest common factor of 697/28,205/5314 = [GCF of 697,205]/[LCM of 28,5314]= 41/74396
Therefore, the GCF of 697/28,205/5314 is 41/74396.
To find the highest common factor of 697,205, we have to find the factors of both numbers and list the highest common factor.
The factors of 697 are 1, 17, 41, 697
The factors of 205 are 1, 5, 41, 205
The HCF of 697,205 is 41.
Lets's calculate GCF of 697,205
| 41 | 697, 205 |
| 17, 5 |
∴ So the GCF of the given numbers is 41 = 41
Greatest Common Factor of 697,205 By Matching Biggest Common Factor Method
Now, list down the factors of 697
:1,17,41,697
Now, list down the factors of 205
:1,5,41,205
Greatest Common Factor
We found the factors 697,205 . The biggest common factor number is the GCF number.
So the greatest common factor 697,205 is 41.
Lets's calculate LCM of 28,5314
| 2 | 28, 5314 |
| 14, 2657 |
∴ So the LCM of the given numbers is 2 x 14 x 2657 = 74396
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 41/74396
Therefore, the GCF of Fractions 697/28,205/5314 is 41/74396
Least Common Multiple of 28,5314 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 28,5314 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(28,5314) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(28,5314) x common factors =2 x 1 = 2
LCM(28,5314) = ( 28 × 5314 ) / 2
LCM(28,5314) = 148792 / 2
LCM(28,5314) = 74396
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FAQs on GCF of Fractions of 697/28, 205/5314
1. What is the HCF of 697,205?
The HCF of 697,205 is 41
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 697/28, 205/5314?
Answer: GCF of Numerators as per given numbers 697/28, 205/5314 is
GCF of Numerators i.e. for 697,205 is 41
LCM of denominators i.e. for 28,5314 is 74396.
Thus, GCF of Fractions is 41/74396.Finally, GCF of Fractions for 697/28, 205/5314 is 41/74396.