Grades 9-10 Video Solutions 2024-2024_9-10

Video Transcription

of the form shown in the diagram. The primes are written in increasing order. Ink has covered some of the primes and some of the exponents. What is the exponent of 17?  First note that because the prime 47 appears, we note that n must be between 47 and 53 inclusive on the 47.  Since 13 to the four is part of the factorization, we know that there are four multiples of three included in n factorial. Then n must be 52 because that's the only way  to get 13 to the four. Then there are three multiples of 17 before 52, and the answer is three.

Video Summary

of the form shown in the diagram. The primes are written in increasing order. Ink has covered some of the primes and some of the exponents. What is the exponent of 17? First note that because the prime 47 appears, we note that n must be between 47 and 53 inclusive on the 47. Since 13 to the four is part of the factorization, we know that there are four multiples of three included in n factorial. Then n must be 52 because that's the only way to get 13 to the four. Then there are three multiples of 17 before 52, and the answer is three.

Keywords

prime factorization

exponent

factorial

multiples

mathematics