Grades 9-10 Video Solutions 2021-video 2021 9-10/28

Video Transcription

Video Summary

The problem involves finding how many 5-digit numbers have digits that multiply to 1000. We start with the prime factorization of 1000: \(2^3\) and \(5^3\). We explore digit combinations like 18555 and 24555, where digits multiply to 1000 without exceeding five digits. Using permutations with repetition, where 5 digits include three identical numbers '5', we calculate the combinations: \(5!\) divided by \(3!\), resulting in 20 arrangements per set. With two sets of digits, there are \(2 \times 20 = 40\) unique numbers. Thus, there are 40 five-digit numbers whose product of digits equals 1000.

Keywords

5-digit numbers

digit multiplication

prime factorization

permutations

unique numbers