Questions: Find the prime factorization of 980. The prime factorization is (Type your answer in factored form)

Find the prime factorization of 980. The prime factorization is (Type your answer in factored form)
Transcript text: Find the prime factorization of 980 . The prime factorization is $\square$ (Type your answer in factored form)
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Solution

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Solution Steps

To find the prime factorization of 980, we need to divide the number by the smallest prime number (2) and continue dividing the quotient by the smallest prime number until we reach 1. The prime factors are the prime numbers we used in the division process.

Step 1: Identify the Smallest Prime Factor

We start by dividing 980 by the smallest prime number, which is 2.

\[ 980 \div 2 = 490 \]

Step 2: Continue Dividing by the Smallest Prime Factor

We continue dividing the quotient by 2 until it is no longer divisible by 2.

\[ 490 \div 2 = 245 \]

Step 3: Move to the Next Smallest Prime Factor

Since 245 is not divisible by 2, we move to the next smallest prime number, which is 3. However, 245 is not divisible by 3, so we move to 5.

\[ 245 \div 5 = 49 \]

Step 4: Continue Dividing by the Next Smallest Prime Factor

Next, we divide 49 by the smallest prime number that divides it, which is 7.

\[ 49 \div 7 = 7 \]

Finally, we divide 7 by 7.

\[ 7 \div 7 = 1 \]

Final Answer

The prime factorization of 980 is:

\[ 980 = 2 \times 2 \times 5 \times 7 \times 7 \]

\(\boxed{2^2 \times 5 \times 7^2}\)

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次の計算をしなさい。 (1) (-2)^3 (2) -5^2 (3) (-3) × 2^2 (4) (2 × 4)^2