Chapter 8, Problem 19SGR

To determine

To Find: Maximum size of square stone that can be used without cutting stone

Answer to Problem 19SGR

Maximum size of square stone that can be used without cutting stone is $12\times 12$ .

Explanation of Solution

Given information:

Length $=120$ inches.

Width $=36$ inches.

Maximum size of square stone that can be used without cutting stone is GCF of 36 and 120

Calculate GCF of 36 and 120 as:

  $36=2\cdot 18$

  $=2\cdot 2\cdot 9$

  $=2\cdot 2\cdot 3$

  $120=2\cdot 60$

  $=2\cdot 2\cdot 2.15$

  $=2\cdot 2\cdot 2\cdot 3\cdot 5$

Therefore GCF of 36 and 120 is $2\cdot 2\cdot 3$

  $=12$ inches