Math / Numbers & Operations

QuestionNumber Theory and Fractions Unit Test
Express the prime factorization of 1,200 as a product of prime numbers with exponents. (2 points)
4. $\square$ $\square$ ${ }^{2}=1,200$ $\square$

Studdy Solution

STEP 1

1. We need to express $1,200$ as a product of prime numbers.
2. The prime factorization should include exponents for repeated prime factors.

STEP 2

1. Identify the smallest prime factor.
2. Divide the number by its smallest prime factor.
3. Repeat the process with the quotient until the quotient is 1.
4. Write the prime factorization using exponents.

STEP 3

Identify the smallest prime factor of $1,200$ . The smallest prime number is $2$ .

STEP 4

Divide $1,200$ by $2$ repeatedly until it is no longer divisible by $2$ .
$1,200 \div 2 = 600$ $600 \div 2 = 300$ $300 \div 2 = 150$ $150 \div 2 = 75$
Now, $75$ is not divisible by $2$ .

STEP 5

Identify the next smallest prime factor of $75$ , which is $3$ .
Divide $75$ by $3$ until it is no longer divisible by $3$ .
$75 \div 3 = 25$
Now, $25$ is not divisible by $3$ .

STEP 6

Identify the next smallest prime factor of $25$ , which is $5$ .
Divide $25$ by $5$ repeatedly.
$25 \div 5 = 5$ $5 \div 5 = 1$

STEP 7

Write the prime factorization using exponents. Count the number of times each prime factor appears:
- $2$ appears $4$ times. - $3$ appears $1$ time. - $5$ appears $2$ times.
Thus, the prime factorization of $1,200$ is:
$2^4 \times 3^1 \times 5^2$
The prime factorization of $1,200$ is:
$\boxed{2^4 \times 3 \times 5^2}$

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QuestionNumber Theory and Fractions Unit Test
Express the prime factorization of 1,200 as a product of prime numbers with exponents. (2 points)
4. $\square$ $\square$ ${ }^{2}=1,200$ $\square$

Studdy Solution

STEP 1

1. We need to express $1,200$ as a product of prime numbers.
2. The prime factorization should include exponents for repeated prime factors.

STEP 2

1. Identify the smallest prime factor.
2. Divide the number by its smallest prime factor.
3. Repeat the process with the quotient until the quotient is 1.
4. Write the prime factorization using exponents.

STEP 3

Identify the smallest prime factor of $1,200$ . The smallest prime number is $2$ .

STEP 4

Divide $1,200$ by $2$ repeatedly until it is no longer divisible by $2$ .
$1,200 \div 2 = 600$ $600 \div 2 = 300$ $300 \div 2 = 150$ $150 \div 2 = 75$
Now, $75$ is not divisible by $2$ .

STEP 5

Identify the next smallest prime factor of $75$ , which is $3$ .
Divide $75$ by $3$ until it is no longer divisible by $3$ .
$75 \div 3 = 25$
Now, $25$ is not divisible by $3$ .

STEP 6

Identify the next smallest prime factor of $25$ , which is $5$ .
Divide $25$ by $5$ repeatedly.
$25 \div 5 = 5$ $5 \div 5 = 1$

STEP 7

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QuestionNumber Theory and Fractions Unit TestExpress the prime factorization of 1,200 as a product of prime numbers with exponents. (2 points)4. □\square□ □\square□ 2=1,200{ }^{2}=1,2002=1,200 □\square□

Studdy Solution

STEP 1

1. We need to express 1,200 1,200 1,200 as a product of prime numbers.2. The prime factorization should include exponents for repeated prime factors.

STEP 2

1. Identify the smallest prime factor.2. Divide the number by its smallest prime factor.3. Repeat the process with the quotient until the quotient is 1.4. Write the prime factorization using exponents.

STEP 3

Identify the smallest prime factor of 1,200 1,200 1,200. The smallest prime number is 2 2 2.

STEP 4

Divide 1,200 1,200 1,200 by 2 2 2 repeatedly until it is no longer divisible by 2 2 2.1,200÷2=600 1,200 \div 2 = 600 1,200÷2=600 600÷2=300 600 \div 2 = 300 600÷2=300 300÷2=150 300 \div 2 = 150 300÷2=150 150÷2=75 150 \div 2 = 75 150÷2=75Now, 75 75 75 is not divisible by 2 2 2.

STEP 5

Identify the next smallest prime factor of 75 75 75, which is 3 3 3.Divide 75 75 75 by 3 3 3 until it is no longer divisible by 3 3 3.75÷3=25 75 \div 3 = 25 75÷3=25Now, 25 25 25 is not divisible by 3 3 3.

STEP 6

Identify the next smallest prime factor of 25 25 25, which is 5 5 5.Divide 25 25 25 by 5 5 5 repeatedly.25÷5=5 25 \div 5 = 5 25÷5=5 5÷5=1 5 \div 5 = 1 5÷5=1

STEP 7

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QuestionNumber Theory and Fractions Unit Test
Express the prime factorization of 1,200 as a product of prime numbers with exponents. (2 points)
4. $\square$ $\square$ ${ }^{2}=1,200$ $\square$

1. We need to express $1,200$ as a product of prime numbers.
2. The prime factorization should include exponents for repeated prime factors.

1. Identify the smallest prime factor.
2. Divide the number by its smallest prime factor.
3. Repeat the process with the quotient until the quotient is 1.
4. Write the prime factorization using exponents.

Identify the smallest prime factor of $1,200$ . The smallest prime number is $2$ .

Divide $1,200$ by $2$ repeatedly until it is no longer divisible by $2$ .
$1,200 \div 2 = 600$ $600 \div 2 = 300$ $300 \div 2 = 150$ $150 \div 2 = 75$
Now, $75$ is not divisible by $2$ .

Identify the next smallest prime factor of $75$ , which is $3$ .
Divide $75$ by $3$ until it is no longer divisible by $3$ .
$75 \div 3 = 25$
Now, $25$ is not divisible by $3$ .

Identify the next smallest prime factor of $25$ , which is $5$ .
Divide $25$ by $5$ repeatedly.
$25 \div 5 = 5$ $5 \div 5 = 1$