3.+Divisors+for+diversion

You now know a lot about divisors. If we asked you to enumerate the divisors of 24, you would write 1, 2, 3, 4, 6, 8, 12, and 24 - a total of 8. Could you say without listing them that 24 has 8 divisors and that 60 has 12? We want you to try and discover a simple rule which helps us to find the number of divisors.

Choose a number and add it to the table and see if you can discover the rule. We have provided you with one example to get you started. Remember n = n 1
 * 1. Number || 2.Divisors ||= 3.Number of divisors ||= 4.Prime factorisation ||= 5.Exponents of primes ||= 6.Exponents + 1 ||= 7.Product of exponents increased by 1 || Comparison of columns 3 and 7 || Name ||
 * 12 || 1,2,3,4,6,12 ||= 6 ||= 2 2 x 3 ||= 2, 1 ||= 3, 2 ||= 6 || The numbers are the same. || James ||
 * 14 || 1,2,7,14 ||= 4 ||= 7x2 ||= 1,1 ||= 2,2 ||= 4 || The numbers are the same. || Paula.V ||
 * 16 || 1,2,4,8,16 ||= 5 ||= 2x2 ﻿3 ||= 1,3 ||= 2,4 ||= 8 || The numbers aren't the same. || Claudia Llenas ||
 * 18 || 1,2,3,6,8,18 ||= 6 ||= 2x3^2 ||= 1,2 ||= 2,3 ||= 6 || The numbers are the same || Marina Massons ||
 * 20 || 10,2,5,1 ||= 4 ||= 2^2 ||= 1,1 ||= 2,2 ||= 4 || The numbers are the same || Clàudia Minguell ||
 * 22 || 1,2,11,22 ||= 4 ||= 2 by 11 ||= 1,1 ||= 2,2 ||= 4 || The numbers are the same || Pau Ferrer ||
 * 26 || 1,2,13,26 ||= 4 ||= 13x2 ||= 1,1 ||= 2,2 ||= 4 || The numbers are the same || Marina.C ||
 * 28 || 1,2,4,7,14,28 ||= 6 ||= 2^2x7 ||= 2,1 ||= 3,2 ||= 6 || The numbers are the same || Oriol M. ||
 * 30 || 1,2,3,5,6,10,15,30 ||= 8 ||= 15x2 ||= 1,1 ||= 2,2 ||= 4 || The numbers aren't the same. || Georgina Roman ||
 * 32 || 1,2,4,8,16,32 ||= 6 ||= 16x2 ||= 1,1 ||= 2,2 ||= 6 || The numbers are the same || Eduard Andreu ||