What is the HCF of 12 and 30?

What is the Highest Common Factor (HCF) of 12 and 30?

The HCF, also known as the greatest common divisor (GCD), is the largest positive integer that divides both 12 and 30 without leaving a remainder. To find the HCF of 12 and 30, we can use various methods such as prime factorization, division method, or Euclid's algorithm.

Let's solve this using the prime factorization method:

First, we need to find the prime factors of 12 and 30.

The prime factors of 12 are 2 and 3, since 12 can be expressed as 2 x 2 x 3.

The prime factors of 30 are 2, 3, and 5, since 30 can be expressed as 2 x 3 x 5.

Next, we need to find the common prime factors:

Both 12 and 30 have the common prime factors 2 and 3.

We can take the product of these common prime factors to find the HCF: HCF = 2 x 3 = 6.

Therefore, the HCF of 12 and 30 is 6.

The HCF represents the largest number that can be evenly divided into both 12 and 30. In other words, if we were to divide both 12 and 30 by 6, there would be no remainder.

Knowing the HCF can be useful in several areas, such as simplifying fractions, finding equivalent fractions, and solving problems involving factors and multiples.

In conclusion, the HCF of 12 and 30 is 6.

What is the LCM and HCF of 12 and 30?

What is the LCM and HCF of 12 and 30?

The LCM (Least Common Multiple) and HCF (Highest Common Factor) are mathematical terms used to find common multiples and factors of two or more numbers.

In the case of 12 and 30, we need to find their LCM and HCF.

The LCM is the smallest number that is divisible by both 12 and 30.

To find the LCM, we can list the multiples of each number:

Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120...

Multiples of 30: 30, 60, 90, 120, 150, 180, 210, 240, 270, 300...

From the lists, we can see that the LCM of 12 and 30 is 60, as it is the smallest number that appears in both lists.

Now, let's find the HCF of 12 and 30.

The HCF is the largest number that divides both 12 and 30 without leaving a remainder.

To find the HCF, we can factorize both numbers:

12 = 2 x 2 x 3

30 = 2 x 3 x 5

The common factors of 12 and 30 are 2 and 3.

Therefore, the HCF of 12 and 30 is 6, as it is the highest common factor.

In conclusion, the LCM of 12 and 30 is 60, while the HCF is 6.

What is the most common factor of 12 and 30?

What is the most common factor of 12 and 30?

When trying to find the most common factor of two numbers, we look for the largest number that can divide both of them evenly. In this case, we have the numbers 12 and 30.

First, we can list the factors of each number. For 12, the factors are: 1, 2, 3, 4, 6, and 12. For 30, the factors are: 1, 2, 3, 5, 6, 10, 15, and 30.

Among these factors, we can identify the common ones:

Both 12 and 30 share the factors 1, 2, 3, and 6. Now, we have to determine the largest number among these common factors.

By comparing the common factors, we see that the largest factor for both 12 and 30 is 6. Therefore, 6 is the most common factor of 12 and 30 since it is the largest number that divides both evenly.

Knowing the most common factor is useful when simplifying fractions or finding the greatest common divisor of two numbers.

Is 12 a factor of 30?

Is 12 a factor of 30?

When considering if 12 is a factor of 30, we must determine if 12 divides evenly into 30. To do this, we need to see if 30 can be divided by 12 without any remainder.

Let's divide 30 by 12:

30 ÷ 12 = 2 remainder 6

Since there is a remainder of 6 when dividing 30 by 12, we can conclude that 12 is not a factor of 30.

If 12 were a factor of 30, there would be no remainder when dividing. However, since there is a remainder of 6, this means that 12 does not divide evenly into 30.

In conclusion, we can state that 12 is not a factor of 30 based on the division result.

What is the HCF of 12 and 36?

What is the HCF of 12 and 36?

The Highest Common Factor or HCF of two or more numbers is the largest positive integer that divides each of the numbers without leaving any remainder.

In this case, we are asked to find the HCF of 12 and 36.

12 can be expressed as 2 * 2 * 3.

36 can be expressed as 2 * 2 * 3 * 3.

In order to find the HCF, we need to identify the common factors between the two numbers and pick the highest one.

The prime factors of 12 are 2 and 3, while the prime factors of 36 are 2 and 3 as well. Therefore, the HCF of 12 and 36 is 2 * 2 * 3, which is equal to 12.

So, the HCF of 12 and 36 is 12.