Explain in your own words how to find the prime factorization of a composite number, using any m

step 1 So let's start with the problem. So here we have to do prime factorization of composite number a

Explain in your own words how to find the prime...

Key Concepts

Composite Numbers

Composite numbers are numbers that have more than two positive divisors. This means aside from 1 and the number itself, they can be evenly divided by other numbers, which makes them suitable to be expressed as products of smaller numbers, often primes.

Prime Numbers

Prime numbers are numbers greater than 1 that have exactly two distinct positive divisors: 1 and the number itself. They serve as the basic building blocks in number theory since every number can be broken down into a product of prime numbers.

Prime Factorization

Prime factorization is the process of breaking down a composite number into a product of prime numbers. According to the Fundamental Theorem of Arithmetic, every integer greater than 1 either is a prime number or can be factored into primes uniquely, disregarding the order of the factors.

Trial Division/Division Method

One effective method for finding the prime factorization is by using trial division, where you repeatedly divide the composite number by the smallest possible prime number until the quotient becomes 1. This method is systematic and ensures that each factor found is prime, and the process is repeated until the composite number is entirely broken down into its prime components.

Transcript

00:07 So let's start with the problem.

00:09 So here we have to do prime factorization of composite number and we can use any method and we have to explain it.

00:16 Okay, so let's start with it.

00:18 The number that i'm going to take is, let me take a composite number.

00:25 I'll take 64.

00:27 Okay, you can take any number.

00:29 Okay, so the first thing is we will find two numbers, okay, which will give product 64 we have to find any two numbers so i'll write 64 i can write 2 into 32 okay so now when you encounter a prime number if you get prime number circle it okay and composite number you have to further break it okay so here i can see 2 is prime number whereas 32 is not a number because 32 has many multiples many factors okay so i will break 32 so 32 i can write it as what i'll do is again 2 into 16 i can write okay so 2 is a prime number so i circle it okay now 16 16 is a composite again i'll split it 16 i can write 2 into 8 2 is a prime number i'll circle it okay now i have 8 i can break 8 as 2 into 4 okay and 2 is prime now i have to break this 4 4 is 2 into 2 so now i am left with 2 and 2 both are primes so we have got these many circles so at the end you have to write composite number equals to product of primes okay that is the one with this circles so i have to write like this so our number was 64 equal to and how many numbers of circles i will have okay i'll write it whatever is in circle i'll write it okay so two into two into two into two into two we had two how many times one two three four five six so one two three four five six okay so we can express it as two into two into two into two okay so this is not decimal this is another way of writing this multiplication i can write it like this okay so five okay so i hope you got the solution this is one kind of method okay and another method is you can go for our division process that's it goes like same okay so this was our first method so we just have to divide it okay okay 64 i'll divide using always you have to start with the least prime number.

03:09 So 2 is it 64 divided 2? yes.

03:12 So i'll do 2.

03:14 When i divide by 64 by 2, i get 32.

03:17 Then if i divide 32, i'll get 16.

03:19 If i divide 16, i'll get 8.

03:21 If i did divide 8, i'll get 4.

03:23 Then i'll divide 4 i'll get 2...