Page 159 - New Medley 5 Semester 1

Z Z Now, circle all other uncrossed numbers.

The circled numbers 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43,

47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97 are primes between 1
and 100.

All the crossed out numbers are composite numbers.

Z Z Twin primes and co-primes

From the primes listed on the previous page, think about the pairs of
primes that have only one composite number between them.

Such pairs are (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), etc.
Such pairs of numbers are called twin primes.

In other words, the two primes differing by 2 are called twin primes.

Consider the common factors of the following pairs of the numbers.

6 and 11 5 and 17 9 and 16

2 3 2
11 5 17 4 8
3
6 1 1 9 1 16

All these pairs have only one common factor, i.e., 1. Such pairs are

called co-primes. A pair of co-primes may have both primes, both
composites or one prime and one composite.

Prime Factorisation

The process of writing a number as a product of its factors is known as

factorisation. When the product has all the factors as prime numbers, they
are called the prime factors.

For example, 24 = 3 × 8 or 2 × 3 × 4 or 4 × 6 or 2 × 12. These are factorisation
of 24.

Prime factorisation of 24 = 2 × 2 × 2 × 3

There are two ways to find the prime factorisation of a number.

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