express the following as a product of their primes:-a)9261
Answers
Answer:
The prime factors are: 3 x 3 x 3 x 7 x 7 x 7
or also written as { 3, 3, 3, 7, 7, 7 }
Written in exponential form: 3cube ×7cubePrime factorization or prime factor decomposition is the process of finding which prime numbers can be multiplied together to make the original number.
Finding the prime factors of 9,261
To find the prime factors, you start by dividing the number by the first prime number, which is 2. If there is not a remainder, meaning you can divide evenly, then 2 is a factor of the number. Continue dividing by 2 until you cannot divide evenly anymore. Write down how many 2's you were able to divide by evenly. Now try dividing by the next prime factor, which is 3. The goal is to get to a quotient of 1.
If it doesn't make sense yet, let's try it...
Here are the first several prime factors: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29...
Let's start by dividing 9,261 by 2
9,261 ÷ 2 = 4,630.5 - This has a remainder. Let's try another prime number.
9,261 ÷ 3 = 3,087 - No remainder! 3 is one of the factors!
3,087 ÷ 3 = 1,029 - No remainder! 3 is one of the factors!
1,029 ÷ 3 = 343 - No remainder! 3 is one of the factors!
343 ÷ 3 = 114.3333 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
343 ÷ 5 = 68.6 - This has a remainder. 5 is not a factor.
343 ÷ 7 = 49 - No remainder! 7 is one of the factors!
49 ÷ 7 = 7 - No remainder! 7 is one of the factors!
7 ÷ 7 = 1 - No remainder! 7 is one of the factors!
The orange divisor(s) above are the prime factors of the number 9,261. If we put all of it together we have the factors 3 x 3 x 3 x 7 x 7 x 7 = 9,261. It can also be written in exponential form as 33 x 73.