What is the square root of 3025 by prime factorisation method
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Answer:
The prime factors are: 5 x 5 x 11 x 11
or also written as { 5, 5, 11, 11 }
Written in exponential form: 52 x 112
Step-by-step explanation:
Prime 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 3,025
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.
Here are the first several prime factors: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29...
Let's start by dividing 3,025 by 2
3,025 ÷ 2 = 1,512.5 - This has a remainder. Let's try another prime number.
3,025 ÷ 3 = 1,008.3333 - This has a remainder. Let's try another prime number.
3,025 ÷ 5 = 605 - No remainder! 5 is one of the factors!
605 ÷ 5 = 121 - No remainder! 5 is one of the factors!
121 ÷ 5 = 24.2 - There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number
121 ÷ 7 = 17.2857 - This has a remainder. 7 is not a factor.
121 ÷ 11 = 11 - No remainder! 11 is one of the factors!
11 ÷ 11 = 1 - No remainder! 11 is one of the factors!
The orange divisor(s) above are the prime factors of the number 3,025. If we put all of it together we have the factors 5 x 5 x 11 x 11 = 3,025. It can also be written in exponential form as 52 x 112.
Here are the first several prime factors: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29...
Let's start by dividing 3,025 by 2
3,025 ÷ 2 = 1,512.5 - This has a remainder. Let's try another prime number.
3,025 ÷ 3 = 1,008.3333 - This has a remainder. Let's try another prime number.
3,025 ÷ 5 = 605 - No remainder! 5 is one of the factors!
605 ÷ 5 = 121 - No remainder! 5 is one of the factors!
121 ÷ 5 = 24.2 - There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number
121 ÷ 7 = 17.2857 - This has a remainder. 7 is not a factor.
121 ÷ 11 = 11 - No remainder! 11 is one of the factors!
11 ÷ 11 = 1 - No remainder! 11 is one of the factors!
The orange divisor(s) above are the prime factors of the number 3,025. If we put all of it together we have the factors 5 x 5 x 11 x 11 = 3,025. It can also be written in exponential form as 52 x 112.