Question
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Answer
250 can be written as \(2 \times 5 \times 5 \times 5\), or \(2 \times 5^3\).
Solution
1. Start with the given number:
\[
250
\]
2. Divide by the smallest prime number \(2\):
\[
250 \div 2 = 125
\]
So,
\[
250 = 2 \times 125
\]
3. Now factor \(125\) by dividing with the prime \(5\):
\[
125 \div 5 = 25
\]
Thus,
\[
125 = 5 \times 25
\]
4. Factor \(25\) similarly:
\[
25 \div 5 = 5
\]
So,
\[
25 = 5 \times 5
\]
5. Combining all the factors, we have:
\[
250 = 2 \times 5 \times 5 \times 5 = 2 \times 5^3
\]
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Simplify this solution Mind Expander
To express 250 as a product of its prime factors, we begin by dividing it by the smallest prime number, which is 2. Since 250 is even, we can divide: 250 ÷ 2 = 125. Next, we move on to the next smallest prime number, which is 3, but 125 is not divisible by 3. Let's try the next prime number, 5: 125 ÷ 5 = 25. We can factor 25 further: 25 ÷ 5 = 5. Finally, we can factor 5, which is already a prime number. Thus, the complete prime factorization of 250 can be expressed as: 250 = 2 × 5 × 5 × 5, or in exponential form, 250 = 2 × 5^3. Now you have it—250 broken down into its prime factors!
