GCF of 822/578, 698/170
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 822/578, 698/170 i.e 2/2890 easily. The following is the detailed procedure to determine the greatest common factor of fractions 822/578, 698/170.
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 822/578,698/170?
Given fractions are 822/578,698/170
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 822/578,698/170, numerators are 822,698
Denominators are 578,170
The GCF of 822,698 is 2 .
LCM of 578,170 is 2890.
The greatest common factor of 822/578,698/170 = [GCF of 822,698]/[LCM of 578,170]= 2/2890
Therefore, the GCF of 822/578,698/170 is 2/2890.
To find the highest common factor of 822,698, we have to find the factors of both numbers and list the highest common factor.
The factors of 822 are 1, 2, 3, 6, 137, 274, 411, 822
The factors of 698 are 1, 2, 349, 698
The HCF of 822,698 is 2.
Lets's calculate GCF of 822,698
| 2 | 822, 698 |
| 411, 349 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 822,698 By Matching Biggest Common Factor Method
Now, list down the factors of 822
:1,2,3,6,137,274,411,822
Now, list down the factors of 698
:1,2,349,698
Greatest Common Factor
We found the factors 822,698 . The biggest common factor number is the GCF number.
So the greatest common factor 822,698 is 2.
Lets's calculate LCM of 578,170
| 2 | 578, 170 |
| 17 | 289, 85 |
| 17, 5 |
∴ So the LCM of the given numbers is 2 x 17 x 17 x 5 = 2890
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/2890
Therefore, the GCF of Fractions 822/578,698/170 is 2/2890
Least Common Multiple of 578,170 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 578,170 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(578,170) = 34
common factors(in case of two or more numbers have common factors) = 1
GCF(578,170) x common factors =34 x 1 = 34
LCM(578,170) = ( 578 × 170 ) / 34
LCM(578,170) = 98260 / 34
LCM(578,170) = 2890
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FAQs on GCF of Fractions of 822/578, 698/170
1. What is the HCF of 822,698?
The HCF of 822,698 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 822/578, 698/170?
Answer: GCF of Numerators as per given numbers 822/578, 698/170 is
GCF of Numerators i.e. for 822,698 is 2
LCM of denominators i.e. for 578,170 is 2890.
Thus, GCF of Fractions is 2/2890.Finally, GCF of Fractions for 822/578, 698/170 is 2/2890.