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Answer :
Final answer:
The highest common factor of 231 and 330 is found by listing all factors of each number, identifying the common factors, and selecting the highest, which is 33.
Explanation:
The highest common factor of two numbers, also known as the greatest common divisor, is the largest number that divides both numbers without leaving a remainder. Let's calculate the highest common factor of 231 and 330. Here are the steps:
- List all the factors of both numbers.
- Find the common factors between the two lists.
- The highest number in this list will be the highest common factor.
The factors for 231 are 1, 3, 7, 11, 21, 33, 77, 231. The factors for 330 are 1, 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 110, 165, 330. So the common factors are 1, 3, 11, 33. Therefore, the highest common factor of 231 and 330 is 33.
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Rewritten by : Jeany
The highest common factor (HCF), also known as the greatest common divisor (GCD), of two numbers is the largest number that divides both of them without leaving a remainder. To find the HCF of 231 and 330, we can use the Euclidean algorithm, which is an efficient method for computing the greatest common divisor.
Here's how you can apply the Euclidean algorithm by hand:
Step 1: Divide the larger number by the smaller number and find the remainder.
330 ÷ 231 = 1 remainder 99
Step 2: Replace the larger number with the smaller number and the smaller number with the remainder from the previous division.
Now, we repeat the process with 231 and 99.
231 ÷ 99 = 2 remainder 33
Step 3: Continue repeating this process, replacing the larger number with the smaller number and the smaller number with the remainder from the previous division.
99 ÷ 33 = 3 remainder 0
When you reach a remainder of 0, the divisor at that step is the HCF of the original two numbers.
In this case, the HCF of 231 and 330 is 33, as the last non-zero remainder was 33. This means that 33 is the largest number that can divide both 231 and 330 without leaving any remainder.
