Please explain how to get the prime factorization in exponent form as in example the number 24. What would be the exponent form?
Thx, J
The factors are 2 and 3. The prime factorization of 24 is (2^3)*3
We would say that 2 has order 3 and 3 has order 1.
what is the prime factorazation
of 34
To find the prime factorization of a number in exponent form, follow these steps:
1. Start by identifying the prime factors of the number. Prime numbers are numbers that are only divisible by 1 and themselves.
2. Divide the number by its smallest prime factor. If the number is divisible evenly, then continue dividing until you can no longer divide evenly.
3. Write down the prime factor and count how many times you divided the number by that factor. This count will become the exponent for that prime factor.
4. Repeat the process with the quotient obtained from the previous step, using the next smallest prime factor. Continue dividing and writing down the factors and their exponents until you reach a quotient of 1.
5. Express the prime factorization using exponent notation. Write down the prime factors raised to their respective exponents, separated by multiplication symbols.
For example, let's find the prime factorization of 24:
1. The prime factors of 24 are 2 and 3.
2. Divide 24 by the smallest prime factor, which is 2:
24 / 2 = 12
3. Write down the prime factor (2) and count how many times we divided by it (1): 2^1
4. Divide the quotient (12) by the next smallest prime factor, which is 2:
12 / 2 = 6
5. Write down the prime factor (2) and count how many times we divided by it (2): 2^2
6. Divide the new quotient (6) by the next prime factor, which is 3:
6 / 3 = 2
7. Write down the prime factor (3) and count how many times we divided by it (1): 3^1
8. The quotient obtained is now 2.
9. Write down the prime factor (2) and count how many times we divided by it (3): 2^3
10. Since the quotient is now 1, we have completed the process.
So, the prime factorization of 24 in exponent form is (2^3) * (3^1), which can also be written as 2^3 * 3.