Question
How many factors of 10 are in each power? Number of factors of 10 in \( 10^{6}: \square \) Number of factors of 10 in \( 10^{4}: ? \)
Ask by Stewart Chan. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Number of factors of 10 in \( 10^{6} \): 6
Number of factors of 10 in \( 10^{4} \): 4
Solution
10⁶ means that the number 10 is multiplied by itself 6 times (i.e., 10⁶ = 10 × 10 × 10 × 10 × 10 × 10). Thus, there are 6 factors of 10 in 10⁶.
Similarly, 10⁴ means 10 is multiplied by itself 4 times, so there are 4 factors of 10 in 10⁴.
So the answers are:
Number of factors of 10 in 10⁶: 6
Number of factors of 10 in 10⁴: 4
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Simplify this solution Mind Expander
To find the number of factors of \( 10 \) in each power, we can use the formula related to prime factorization. Since \( 10 = 2 \times 5 \), the number of factors of \( 10^n \) is directly equal to \( n \). So, for \( 10^6 \), the number of factors of \( 10 \) is \( 6 \). For \( 10^4 \), the number of factors of \( 10 \) is \( 4 \). Thus, we have: Number of factors of \( 10 \) in \( 10^{6}: 6 \) Number of factors of \( 10 \) in \( 10^{4}: 4 \)
