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5.2 Prime Numbers

Guna and Arahu want to pack figs (angeer) that grow in their farm. Guna wants to put 12 figs in each box and Anthu wants to put 7 figs in each box.

How many arrangements are posible? Think and find out the different ways how

Gune can arrange 12 figs in a rectangular marmer il. Anshu can arrange 7 figs in a rectangular manner.

Guna has listed out these possibilities Observe the number of rows and

columns in each of the arrangements. How are they rulated to 127

In the second arrangement, for example, 12 figs are arranged in twe columns of 6 each or 12-26 Ambu could make only one arrangement: 7x1 or 17. There are no other rectangular arrangements possible.

In each of Gana's arrangements, multiplying the number of rows hy the cumber culumas gives the number 12. 5o, the number of rows or columns are factmes of 12.

We saw that the number mumber 12. 12. can he arranged u rectangle more than one way as 12 has more than two factors. The number 7 can be arranged in unly one way, as it has only two factors-1 and 7, Numbers that have only two factors are called prime numbers or primes. Here are the first few primes 2, 3, 5, 7, 11, 13, 17, 19. Notice that the factors of a prime e number are 1 and the number itself What about numbers that have more than two factors? They called composite numbers. The Best -4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20 composite numbers

which has only one factor? The number 1 is neither composite number. a prin

How many prime number composite numbers there from 21 to 30? How many rom 21 to 307

Can we list all the prime numbers from 1 to 1007 Here Interesting way to find prime numbers just follow the steps given below and see what happens.

Step 1: Cross cut 1 because it is neither prime nor composite. ep 2: Circle 2, and then en cross cross Step 2

nut all multiples of 2 after that. on. Step 3: You will find that the next uncrossed number Circle 3 and then cross out all 60

DUNKTX

2024 20

the multiples of 1 after that,

Le, 6, 9, 12 and so on. Step & The next uncromed

number is 5. Clecie 5 and then trous out all the multiples of after that, ie, 10, 15, 20 and so on multiples ofs

Step 5: Continue this process till all the numbers in the list are either. All the circled numbers are prime

circled or crussed out.

numbers. All the crossed out numbers.

uther than 1, are composite numbers. This method is talled the Sieve of Eratosthenes Eratosthenes This procedure can carried on for numbers greater 100 alsa Eratosthenes was a Greek mathematician who lived around 2200 years ago and developed this method of listing primes.

Guna and Anshu started wondering how this simpir method able to find prime numbers! Think how this method works. Read the stept given above again and see what happens after sach step is carried out.

Figure it Out 1. We that 2 is a prime and also an even number. h there any other even prime

list of primes till between two acessive primes? What allest difference. largest differsnort Are there an equal number of primes nccurring in row in the maniber table on the previous page? Which decades have the least wan of prines? Which have the n he most number of primes

Primes through the Ages

Prime number the building og hincks of sil whole nombers. Starting from the time of the Greek civilinatum (more than 2000 years ago t this day, mathematicians are still straggling to uncover their semen Food for thought: thece a largest prime number? Or dues the le of prime numbers go us without an end? A mathematician named Euclid found the answer and will you in a later dast Fun fact: The largest priame number that anyone has wrimen down is a large that it would take around 6500 pages could