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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:
  • Factor of 8 = 1, 2, 4, and 8.

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

  • 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:
  • 1, 2, and 4.

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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.

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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.

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Step 2:

Find the prime factorization of 16.

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Step 3:

Encircle the common prime factors.

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Step 4:

Multiply the common prime factors.

2 × 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.
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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.

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HCF = 2 × 2

      = 4

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

Fun Facts:

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Did you know?

An English Mathematician, William Oughtred invented the symbol “×” for multiplication.

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