How to find the gcd of three numbers?
Understand the Problem
The question is asking for the method to find the greatest common divisor (gcd) of three given numbers. This typically involves finding the gcd in pairs or using the prime factorization method.
Answer
The greatest common divisor of 60, 48, and 36 is $12$.
Answer for screen readers
The greatest common divisor (gcd) of 60, 48, and 36 is $12$.
Steps to Solve
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Identify the Numbers Start by clearly identifying the three numbers for which you want to calculate the gcd. For example, let’s say the numbers are 60, 48, and 36.
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Find the GCD of the First Two Numbers Use the Euclidean algorithm to find the gcd of the first two numbers. The algorithm involves repeated division:
For our example:
- Divide 60 by 48, which gives a remainder of 12.
- Then, divide 48 by 12 (which gives a remainder of 0).
Thus, $gcd(60, 48) = 12$.
- Find the GCD with the Third Number Now use the result from the previous step and apply the gcd with the third number using the same method:
For our example:
- Compute $gcd(12, 36)$.
- Divide 36 by 12, which gives a remainder of 0.
Thus, $gcd(12, 36) = 12$.
- Final GCD Result The final result after finding the gcd of all three numbers is 12. Therefore, the greatest common divisor of 60, 48, and 36 is 12.
The greatest common divisor (gcd) of 60, 48, and 36 is $12$.
More Information
The greatest common divisor represents the largest number that divides all the given numbers without any remainder. It can be useful in simplifying fractions and solving problems regarding ratios.
Tips
- Forgetting to apply the gcd method to all three numbers sequentially. Ensure to follow up the result from the first pair with the next number.
- Incorrect division or miscalculating the remainder during the Euclidean algorithm steps. Double-check calculations at each step to avoid simple arithmetic errors.
