WHOLE NUMBERS

CONTENT

1. Revision: Prime Factors, LCM and HCF
2. Squares and Square Roots
3. Quantitative Reasoning

Prime Factors, LCM and HCF

Prime Factors of Numbers

Prime factors of a number are the factors of that number that are not divisible by any other number except that number and \(1\). For example, the prime factors of \(30\) are \(2\), \(3\) and \(5\) because out of all the factors of \(30\) \((1, 2, 3, 5, 6, 10, 15\) and \(30)\), it is only \(2, 3\) and \(5\) that are not divisible by any other number except themselves and \(1\).

Examples:

Write the factors of the following numbers and state the prime factors, hence express each number as a product of its prime factors.

(a) \(22\) (b) \(50\) (c) \(63\) (d) \(42\)

Solutions:                       

(a) \(22\)

Factors of \(22\) are \(1, 2, 11, 22\)

The prime factors of \(22\) are \(2\) and \(11\)

Product of its prime factors of \(22 = 2 × 11\)

(b) Factors of \(50\) are \(1, 2, 5, 10, 25\) and \(50\)

The prime factors of \(50\) are \(2\) and \(5\)

Product of its prime factors of \(50 = 2 × 5 × 5 = 2 × 5^2\)

(c) Factors of \(63\) are \(1, 3, 7, 9, 21\) and \(63\)

The prime factors of \(63\) are \(3\) and \(7\)

Product of its prime factors of \(63 = 3 × 3 × 7 = 3^2 × 7\)

(d) Factors of \(42\) are \(1, 2, 3, 6, 7, 14, 21\) and \(42\)

The prime factors of \(42\) are \(2, 3\) and \(7\)

Product of its prime factors of \(42 = 2 × 3 × 7\)

Prime Factorization

Examples

Express the following as a product of their prime factors in index form.