Solved on Nov 19, 2023

Find the prime factorization of 90 using exponents.

STEP 1

Assumptions1. We are asked to find the prime decomposition of90 in index form. . Prime decomposition, also known as prime factorization, is the process of determining the prime numbers that multiply together to make a certain number.
3. In index form, the prime factors are written with exponents.

STEP 2

First, we need to find the prime factors of90. We can do this by dividing90 by prime numbers, starting from the smallest prime number, which is2.

STEP 3

Divide90 by2. If the quotient is a whole number, then2 is a prime factor of90.
$90 /2 =45$

STEP 4

Now, divide the quotient45 by the next prime number, which is3. If the quotient is a whole number, then3 is a prime factor of45.
$45 /3 =15$

STEP 5

Again, divide the new quotient15 by3. If the quotient is a whole number, then3 is a prime factor of15.
$15 /3 =5$

STEP 6

Finally, divide the new quotient5 by the next prime number, which is5. If the quotient is a whole number, then5 is a prime factor of5.
$5 /5 =1$

STEP 7

Now that we have found all the prime factors of90, we can write them out. The prime factors of90 are2,3,3, and5.

STEP 8

To write the prime decomposition in index form, we write the prime factors with their corresponding exponents. The exponent is the number of times the prime factor divides the original number.
The prime decomposition of90 in index form is $90 =2^1 \times3^2 \times5^1$

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Find the prime factorization of 90 using exponents.

STEP 1

Assumptions1. We are asked to find the prime decomposition of90 in index form. . Prime decomposition, also known as prime factorization, is the process of determining the prime numbers that multiply together to make a certain number.
3. In index form, the prime factors are written with exponents.

STEP 2

First, we need to find the prime factors of90. We can do this by dividing90 by prime numbers, starting from the smallest prime number, which is2.

STEP 3

Divide90 by2. If the quotient is a whole number, then2 is a prime factor of90.
$90 /2 =45$

STEP 4

Now, divide the quotient45 by the next prime number, which is3. If the quotient is a whole number, then3 is a prime factor of45.
$45 /3 =15$

STEP 5

Again, divide the new quotient15 by3. If the quotient is a whole number, then3 is a prime factor of15.
$15 /3 =5$

STEP 6

Finally, divide the new quotient5 by the next prime number, which is5. If the quotient is a whole number, then5 is a prime factor of5.
$5 /5 =1$

STEP 7

Now that we have found all the prime factors of90, we can write them out. The prime factors of90 are2,3,3, and5.

STEP 8

To write the prime decomposition in index form, we write the prime factors with their corresponding exponents. The exponent is the number of times the prime factor divides the original number.
The prime decomposition of90 in index form is $90 =2^1 \times3^2 \times5^1$

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Find the prime factorization of 90 using exponents.

STEP 1

Assumptions1. We are asked to find the prime decomposition of90 in index form. . Prime decomposition, also known as prime factorization, is the process of determining the prime numbers that multiply together to make a certain number.3. In index form, the prime factors are written with exponents.

STEP 2

First, we need to find the prime factors of90. We can do this by dividing90 by prime numbers, starting from the smallest prime number, which is2.

STEP 3

Divide90 by2. If the quotient is a whole number, then2 is a prime factor of90.90/2=4590 /2 =4590/2=45

STEP 4

Now, divide the quotient45 by the next prime number, which is3. If the quotient is a whole number, then3 is a prime factor of45.45/3=1545 /3 =1545/3=15

STEP 5

Again, divide the new quotient15 by3. If the quotient is a whole number, then3 is a prime factor of15.15/3=515 /3 =515/3=5

STEP 6

Finally, divide the new quotient5 by the next prime number, which is5. If the quotient is a whole number, then5 is a prime factor of5.5/5=15 /5 =15/5=1

STEP 7

Now that we have found all the prime factors of90, we can write them out. The prime factors of90 are2,3,3, and5.

STEP 8

To write the prime decomposition in index form, we write the prime factors with their corresponding exponents. The exponent is the number of times the prime factor divides the original number.The prime decomposition of90 in index form is90=21×32×5190 =2^1 \times3^2 \times5^190=21×32×51

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Assumptions1. We are asked to find the prime decomposition of90 in index form. . Prime decomposition, also known as prime factorization, is the process of determining the prime numbers that multiply together to make a certain number.
3. In index form, the prime factors are written with exponents.

Divide90 by2. If the quotient is a whole number, then2 is a prime factor of90.
$90 /2 =45$

Now, divide the quotient45 by the next prime number, which is3. If the quotient is a whole number, then3 is a prime factor of45.
$45 /3 =15$

Again, divide the new quotient15 by3. If the quotient is a whole number, then3 is a prime factor of15.
$15 /3 =5$

Finally, divide the new quotient5 by the next prime number, which is5. If the quotient is a whole number, then5 is a prime factor of5.
$5 /5 =1$

To write the prime decomposition in index form, we write the prime factors with their corresponding exponents. The exponent is the number of times the prime factor divides the original number.
The prime decomposition of90 in index form is $90 =2^1 \times3^2 \times5^1$