Math / Numbers & Operations

QuestionFind the prime factorization of each composite number. Write your final answer using exponents.
3. 960 (5pts)

Studdy Solution

STEP 1

1. The number to be factorized is $960$ .
2. We need to find the prime factors of $960$ .
3. The final answer should be expressed using exponents.

STEP 2

1. Divide by the smallest prime number.
2. Continue dividing by prime numbers.
3. Write the prime factorization using exponents.

STEP 3

Start by dividing $960$ by the smallest prime number, which is $2$ .
$960 \div 2 = 480$

STEP 4

Continue dividing the result by $2$ until it is no longer divisible by $2$ .
$480 \div 2 = 240$ $240 \div 2 = 120$ $120 \div 2 = 60$ $60 \div 2 = 30$ $30 \div 2 = 15$

STEP 5

Now, divide by the next smallest prime number, which is $3$ .
$15 \div 3 = 5$

STEP 6

Finally, divide by the next smallest prime number, which is $5$ .
$5 \div 5 = 1$

STEP 7

Write the prime factorization of $960$ using exponents. Count the number of times each prime number is used in the factorization.
- The prime number $2$ is used $6$ times. - The prime number $3$ is used $1$ time. - The prime number $5$ is used $1$ time.
Thus, the prime factorization of $960$ is:
$960 = 2^6 \times 3^1 \times 5^1$
The prime factorization of $960$ is:
$\boxed{2^6 \times 3 \times 5}$

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QuestionFind the prime factorization of each composite number. Write your final answer using exponents.
3. 960 (5pts)

Studdy Solution

STEP 1

1. The number to be factorized is $960$ .
2. We need to find the prime factors of $960$ .
3. The final answer should be expressed using exponents.

STEP 2

1. Divide by the smallest prime number.
2. Continue dividing by prime numbers.
3. Write the prime factorization using exponents.

STEP 3

Start by dividing $960$ by the smallest prime number, which is $2$ .
$960 \div 2 = 480$

STEP 4

Continue dividing the result by $2$ until it is no longer divisible by $2$ .
$480 \div 2 = 240$ $240 \div 2 = 120$ $120 \div 2 = 60$ $60 \div 2 = 30$ $30 \div 2 = 15$

STEP 5

Now, divide by the next smallest prime number, which is $3$ .
$15 \div 3 = 5$

STEP 6

Finally, divide by the next smallest prime number, which is $5$ .
$5 \div 5 = 1$

STEP 7

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QuestionFind the prime factorization of each composite number. Write your final answer using exponents.3. 960 (5pts)

Studdy Solution

STEP 1

1. The number to be factorized is 960 960 960.2. We need to find the prime factors of 960 960 960.3. The final answer should be expressed using exponents.

STEP 2

1. Divide by the smallest prime number.2. Continue dividing by prime numbers.3. Write the prime factorization using exponents.

STEP 3

Start by dividing 960 960 960 by the smallest prime number, which is 2 2 2.960÷2=480 960 \div 2 = 480 960÷2=480

STEP 4

Continue dividing the result by 2 2 2 until it is no longer divisible by 2 2 2.480÷2=240 480 \div 2 = 240 480÷2=240 240÷2=120 240 \div 2 = 120 240÷2=120 120÷2=60 120 \div 2 = 60 120÷2=60 60÷2=30 60 \div 2 = 30 60÷2=30 30÷2=15 30 \div 2 = 15 30÷2=15

STEP 5

Now, divide by the next smallest prime number, which is 3 3 3.15÷3=5 15 \div 3 = 5 15÷3=5

STEP 6

Finally, divide by the next smallest prime number, which is 5 5 5.5÷5=1 5 \div 5 = 1 5÷5=1

STEP 7

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QuestionFind the prime factorization of each composite number. Write your final answer using exponents.
3. 960 (5pts)

1. The number to be factorized is $960$ .
2. We need to find the prime factors of $960$ .
3. The final answer should be expressed using exponents.

1. Divide by the smallest prime number.
2. Continue dividing by prime numbers.
3. Write the prime factorization using exponents.

Start by dividing $960$ by the smallest prime number, which is $2$ .
$960 \div 2 = 480$

Continue dividing the result by $2$ until it is no longer divisible by $2$ .
$480 \div 2 = 240$ $240 \div 2 = 120$ $120 \div 2 = 60$ $60 \div 2 = 30$ $30 \div 2 = 15$

Now, divide by the next smallest prime number, which is $3$ .
$15 \div 3 = 5$

Finally, divide by the next smallest prime number, which is $5$ .
$5 \div 5 = 1$