Prime factorize the following using factor tree method:
66, 99, 20, 108, 37 and 450
66 = 2*33 = 2 * 3 * 11
99 = 3 * 33 = 3 * 3 * 11
20 = 2*10 = 2 * 2 * 5
etc, boring
22 x 5 = 99.
20 is not a prime number.
The prime factorization for 66: Prime factorization is writing a composite number as a product of its prime factors.
Sample A:
The prime factorization of 504 is 2^3 x 3^2 x 7.
In other words, it is a way of writing a product the long way.
Sample B:
The prime factorization of 30 is 2 x 3 x 5.
Your question:
The Prime Factorization of 66.
What is the biggest number that goes into 66 without a remainder?
How about 11?
11 x 6 = 66, right?
We cannot break down 11 anymore but it is one of our composite numbers that we used as a factor of 66.
What about 6?
What are the factors of 6?
How about 2 and 3?
Yes, 2 x 3 = 6.
We cannot break down 2 and 3 anymore.
Final answer: The prime factorization of 66 is: 2 x 3 x 11.
That's it!
Prime factorization of 99 is: To learn the prime factors of 99, find two numbers that multiply together to make 99, such as 9 and 11. Eleven is a prime factor because it is only divisible by itself and 1, but 9 is not prime. Next, find two numbers that multiply together to make 9, such as 3 times 3. Since 3 is prime, all the prime factors have been found.
Answer : 22 • 5. 20 is NOT a prime number.
I don't have enough room to work out 108, 37 and 450.
To prime factorize a number using the factor tree method, we repeatedly divide the number into its prime factors until only prime numbers remain. Let's apply this method to each of the given numbers:
1. Prime factorization of 66:
Start with the number 66. We can divide it by the smallest prime number, which is 2:
66 / 2 = 33
Now, we focus on the quotient 33. Again, we divide it by the smallest prime number, which is 3:
33 / 3 = 11
Since 11 is a prime number, we have completed the prime factorization of 66:
66 = 2 * 3 * 11
2. Prime factorization of 99:
Start with the number 99. We can divide it by the smallest prime number, which is 3:
99 / 3 = 33
Now, we focus on the quotient 33. Again, we divide it by the smallest prime number, which is 3:
33 / 3 = 11
Since 11 is a prime number, we have completed the prime factorization of 99:
99 = 3 * 3 * 11
3. Prime factorization of 20:
Start with the number 20. We can divide it by the smallest prime number, which is 2:
20 / 2 = 10
Now, we focus on the quotient 10. Again, we divide it by the smallest prime number, which is 2:
10 / 2 = 5
Since 5 is a prime number, we have completed the prime factorization of 20:
20 = 2 * 2 * 5
4. Prime factorization of 108:
Start with the number 108. We can divide it by the smallest prime number, which is 2:
108 / 2 = 54
Now, we focus on the quotient 54. Again, we divide it by the smallest prime number, which is 2:
54 / 2 = 27
Now, we focus on the quotient 27. Again, we divide it by the smallest prime number, which is 3:
27 / 3 = 9
Now, we focus on the quotient 9. Again, we divide it by the smallest prime number, which is 3:
9 / 3 = 3
Since 3 is a prime number, we have completed the prime factorization of 108:
108 = 2 * 2 * 3 * 3 * 3
5. Prime factorization of 37:
37 is a prime number itself, so its prime factorization is simply 37:
37 = 37
6. Prime factorization of 450:
Start with the number 450. We can divide it by the smallest prime number, which is 2:
450 / 2 = 225
Now, we focus on the quotient 225. Again, we divide it by the smallest prime number, which is 3:
225 / 3 = 75
Now, we focus on the quotient 75. Again, we divide it by the smallest prime number, which is 3:
75 / 3 = 25
Now, we focus on the quotient 25. Again, we divide it by the smallest prime number, which is 5:
25 / 5 = 5
Since 5 is a prime number, we have completed the prime factorization of 450:
450 = 2 * 3 * 3 * 5 * 5