What is the highest common factor of 330?

The highest common factor (HCF) of 330 is the largest number that can divide both 330 and another given number without leaving any remainder. To find the HCF of 330, we need to factorize it into its prime factors.

First, let's start by listing the prime factors of 330. To do this, we divide 330 by the smallest possible prime number, which is 2. Since 330 is an even number, it is divisible by 2. 330 ÷ 2 = 165.

Now, we continue factoring 165. Again, we divide it by 2 as it is still an even number. 165 ÷ 2 = 82.5. However, we cannot have a fraction as a factor, so 2 is not a factor of 165.

Next, we move on to the next prime number, which is 3. We seek to divide 165 by 3. 165 ÷ 3 = 55.

Now, 55 is an odd number, so we need to continue factoring it by dividing it with the next smallest prime number, which is 5. 55 ÷ 5 = 11.

Finally, we have factored 330 into its prime factors, which are 2, 3, 5, and 11. The prime factorization of 330 is 2 x 3 x 5 x 11.

To find the HCF of 330, we look for the highest common factor among the prime factors. In this case, since there are no other prime factors mentioned, the HCF is simply the product of the common prime factors, which is 2 x 3 x 5 x 11 or 330.

Therefore, 330 is the highest common factor of itself.

What is the highest common factor 330 and 385?

What is the highest common factor of 330 and 385?

The highest common factor, also known as the greatest common divisor, is the largest number that divides two given numbers without leaving any remainder.

First, let's find the prime factors of both 330 and 385. Prime factors are the prime numbers that can be multiplied together to obtain the original number.

330 can be factored as 2 * 3 * 5 * 11, while 385 can be factored as 5 * 7 * 11.

Now, let's find the common factors of 330 and 385.

The common factors of 330 and 385 are 5 and 11.

To find the highest common factor, we need to find the greatest common factor among the common factors.

The highest common factor of 330 and 385 is 11, as it is the largest number that divides both 330 and 385 without leaving any remainder.

Therefore, the highest common factor of 330 and 385 is 11.

What's the highest common factor of 330 and 231?

The highest common factor of 330 and 231 is the largest number that can divide both 330 and 231 without leaving a remainder. In order to find the highest common factor, we need to identify the factors of both numbers and determine the highest common factor between them.

Firstly, let's identify the factors of 330. We can start by finding the prime factorization of 330. By dividing 330 by its smallest prime factor, which is 2, we get 165. Then, by dividing 165 by its smallest prime factor, which is 3, we get 55. Finally, dividing 55 by its smallest prime factor, which is also 5, we end up with 11. Therefore, the prime factorization of 330 is 2 * 3 * 5 * 11.

Secondly, let's identify the factors of 231. By dividing 231 by its smallest prime factor, which is 3, we get 77. Then, by dividing 77 by its smallest prime factor, which is 7, we end up with 11. Therefore, the prime factorization of 231 is 3 * 7 * 11.

Finally, we can now determine the highest common factor of 330 and 231 by identifying the common prime factors between the two numbers. Since both numbers have the prime factor 11, and there are no other common prime factors, the highest common factor of 330 and 231 is 11.

What is the HCF of 330 and 66?

What is the HCF of 330 and 66?

The highest common factor (HCF), also known as the greatest common divisor (GCD), is the largest positive integer that divides both 330 and 66 without leaving a remainder. To find the HCF of 330 and 66, we can use various methods, including prime factorization, division, or Euclid's algorithm.

First, let's explore the prime factorization method.

To find the prime factorization of 330, we divide it by prime numbers starting from 2. By dividing 330 by 2, we get 165. In turn, 165 can also be divided by 3, resulting in 55. Further dividing 55 by 5 gives us 11, which is a prime number. Hence, the prime factorization of 330 is 2 × 3 × 5 × 11.

Similarly, to find the prime factorization of 66, we divide it by 2, which gives us 33. Dividing 33 by 3 results in 11. Therefore, the prime factorization of 66 is 2 × 3 × 11.

Now that we have the prime factorizations, we can identify the common factors.

The common factors of 330 and 66 are the prime factors that they both share. From their prime factorizations, we can see that the common factors are 2, 3, and 11. As the HCF is the highest common factor, we select the highest among these common factors, which is 11.

Therefore, the HCF of 330 and 66 is 11.

The HCF is useful in various mathematical calculations, such as simplifying fractions, finding equivalent fractions, and solving problems related to divisibility. By finding the HCF of two numbers, we can find the greatest common divisor that can divide both numbers without leaving a remainder.

In conclusion, the HCF of 330 and 66 is 11, which is the highest common factor of the two numbers.

How do you find the highest common factor?

Finding the highest common factor (HCF) of two or more numbers can be done through various methods. One of the most commonly used techniques is the prime factorization method.

This method involves breaking down each number into its prime factors. By finding the prime factors of each number, you can determine which factors are common to all of them. The highest common factor is then found by multiplying these common factors together.

Another approach to find the HCF is through the use of division method. This method involves dividing the larger number by the smaller number repeatedly until the remainder is zero. The divisor used in each division is then the common factor. By continuing this process, you can find the highest common factor of the given numbers.

Euclid's algorithm is another commonly used method to find the HCF. It involves successive division and is based on the principle that the highest common factor of two numbers remains the same if the larger number is replaced by its difference with the smaller number. The process is repeated until the remainder is zero, and the divisor used at the last step is the highest common factor.

In conclusion, there are various methods to find the highest common factor of given numbers. These methods include prime factorization, division method, and Euclid's algorithm. Each method has its advantages and can be used depending on the specific situation. By applying one of these techniques, you can effectively determine the highest common factor of any set of numbers.

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