Grades 9-10 Video Solutions 2025-2025_9-10

Video Transcription

Video Summary

To find the largest 6-digit number with a product of digits equal to 180, we start by maximizing each digit, beginning with the largest. The prime factorization of 180 is \(2^2 \times 3^2 \times 5\). The largest digit dividing 180 is 9, making the first digit 9. Dividing 180 by 9 leaves 20 for the product of the remaining digits. The largest divisor of 20 is 5, so the second digit is 5. With 4 remaining, the third digit becomes 4. The last three digits, multiplying to 1, are all 1s. The digits are 9, 5, 4, 1, 1, 1, summing to 21.

Keywords

largest number

6-digit

product of digits

factorization

180