Grades 11-12 Video Solutions 2021-video 2021 11-12/11

Video Transcription

Video Summary

The video discusses calculating the proportion of odd divisors of 7 factorial. First, it explains the process for finding the number of divisors using prime factorization: multiply one more than each of the prime exponents together. Applying this to 7 factorial yields 60 total divisors. To find odd divisors, remove even factors, leaving primes contributing to odd products. For 7 factorial, recalculating with only odd factors gives 12 odd divisors. The proportion of odd divisors to total divisors is 12 out of 60, simplifying to 1 in 5. Thus, the answer to the problem is one in five.

Keywords

odd divisors

7 factorial

prime factorization

proportion

mathematics