**Factors and Multiples**

HCF

- The factors of a number are those numbers that are exactly divisible by the given number.
- The common factor of the number are the factors that are common to the two or more numbers.

Example:

- The factor of the numbers 8 and 12 are:
- The common factors of 8 and 12 are the list of the numbers which is common in the factors of 8 and 12.
- Therefore, the
**common factors**of 8 and 12 are:

Factor of 8 = 1, 2, 4, and 8.

Factor of 12 = 1, 2, 3, 4, 6, and 12.

1, 2, and 4.

Highest Common Factor

- The highest common factor is the largest of the common factors.
- It is also known as the
**greatest common divisor**. - It is also written as HCF or GCD

Methods to find the HCF

- Common factors method
- Prime factorization method
- Division method

Common Factors method

- Write the factors of the numbers.
- List the common factors of the numbers.
- Choose the largest common factor.

Example:

Find the highest common factor of 8 and 12.

Solution:

Factor of 8 = 1, 2, 4, and 8.

The factors of 12: 1, 2, 3, 4, 6, and 12.

The common factors of 8 and 12 are: 1, 2, and 4.

The largest common factor of 8 and 12 is 4. Therefore, HCF or the highest common factor of 8 and 12 is 4.

Prime Factorization method

- Write the prime factorization of each number.
- Circle the common prime factors.
- Multiply the common prime factors.
- The obtained product is equal to the HCF of the numbers.

Example:

Find the HCF of 12 and 16.

Solution:

Step 1:

Find the prime factorization of 12.

Step 2:

Find the prime factorization of 16.

Step 3:

Encircle the common prime factors.

Step 4:

Multiply the common prime factors.

2 Ă— 2 = 4

Therefore, the highest common factor or HCF of 12 and 16 is 4.

Division method

- Divide the larger number by the smaller number.
- Divide the divisor by the remainder.
- Repeat the process of dividing the divisor by the remainder until you get 0 as the remainder.
- The last obtained divisor is the HCF of the numbers.

Example:

Find the HCF of 20 and 36.

Solution:

- Divide 36 by 20.
- Divide 20 by 16.
- Divide 16 by 4.

Since the last remainder is 0 therefore, the last divisor is equal to the HCF of 20 and 36.

HCF = 4

Word Problem:

Example:

There are 12 girls and 8 boys in the class. The teacher wants to place them in equal rows. Find the greatest number of students who can be in each row.

Solution:

Number of girls = 12

Number of boys = 8

Obtain the greatest common factor of 12 and 8.

HCF = 2 Ă— 2

= 4

Therefore, the greatest number of students in each row is 4.

Fun Facts:

Did you know?

An English Mathematician, William Oughtred invented the symbol â€śĂ—â€ť for multiplication.