Answer to Question #192288 in Combinatorics | Number Theory for Brian McMahon

Question

How many different rectangles can be made, whose side lengths in centimeters are counting numbers and whose area is 1159 cm2.?

Answer 1

find the factors of 1159

$1159=1\times1159$

$1159=19\times61$

factors of 1159 are; 1, 19, 61, 1159

the rectangles whose area is $1159cm^2$ are;

$1) length=1159cm, width=1cm$

$2) length=61cm, width=19cm$

Hence only 2 rectangles can be made