Divisibility. Prime factorization. GCF and LCM.
Think about these problems by Thur, March 6; Written solutions are due by Tues, March 11.

Question 1. Using divisibility tests by 2, 3, 4, 5, and 9, explain how to determine whether a number is divisible by

• 6;
• 12;
• 15;
• 18.

Question 2. Which of the following numbers divide the number 2,010?

6,   12,   15,   18

Question 3. Which of the following numbers divide the number 1,245?

6,   12,   15,   18

Question 4. Find prime factorizations of 2,010 and 1,245.

Question 5. Find the greatest common factor and the least common multiple of 2,010 and 1,245.

Important: In questions 2 and 3, provide an explanation for each answer! Correct answer without explanation will not receive full credit.
Examples of explanations: The number 4005 is not divisible by 6 because it is not divisible by 2. The number 4005 is divisible by 15 since it is divisible by both 3 and 5.

Additional problems discussed in class (not part of written homework)

Problem 1. The GCF of 66 and x is 11; the LCM of 66 and x is 858. Find x.

Problem 2. The GCF of two numbers m and n is 12, their LCM is 600, and both m and n are less than 500. Find m and n.