Find four positive integers, each not exceeding 70000 and each having more than 100 divisors.


Question and Answers Forum

All Questions Topic List
Number Theory Questions
Previous in All Question Next in All Question
Previous in Number Theory Next in Number Theory
Question Number 200200 by Fridunatjan08 last updated on 16/Nov/23

$F i n d f o u r p o s i t i v e i n t e g e r s,$ $e a c h n o t e x c e e d i n g 70000 a n d$ $e a c h h a v i n g m o r e t h a n 100$ $d i v i s o r s .$
	Answered by mr W last updated on 16/Nov/23

	$e x a m p l e s :$ $50400 h a s 108 d i v i s o r s$ $55440 h a s 120 d i v i s o r s$ $60480 h a s 112 d i v i s o r s$ $65520 h a s 120 d i v i s o r s$ $69300 h a s 108 d i v i s o r s$ $. . . . . .$
	Commented by mr W last updated on 17/Nov/23

	$s e e a l s o e x p l a n a t i o n f r o m MM 42 s i r$ $You can't use 'macro parameter character #' in math mode$
	Commented by Fridunatjan08 last updated on 16/Nov/23

	$b u t h o w t o f i n d t h e s e n u m b e r s ?$
	Commented by mr W last updated on 17/Nov/23

	$t h e n u m b e r c a n b e e x p r e s s e d a s$ $2^{a} \times 3^{b} \times 5^{c} \times 7^{d} \times 11^{e} \times . . .$ $n o w y o u s e l e c t a, b, c, d, e, . . . s u c h t h a t$ $2^{a} \times 3^{b} \times 5^{c} \times 7^{d} \times 11^{e} \times . . . < 70000 a n d$ $(a + 1) (b + 1) (c + 1) (d + 1) (e + 1) . . . > 100$ $w e m u s t ‘ ‘ e r r o r a n d {t r y}^{″}!$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum