Question

How do the ideas of divisibility and multiples relate to the study of fractions?

Show that 1,078 and 3,315 are relatively prime.

What is the shortest length of television cable that could be cut into either a whole number of 18-ft pieces or a whole number of 30-ft pieces?

When finding the factors of 841, what is the largest factor you would have to test? What theorem supports this?

Find the LCM of the numbers 24 and 32 by using:

a. the listing multiples method.





b. the prime factorization method.

The product of two numbers is 180. The LCM of the two numbers is 60. What is the GCF of the numbers?


Explain how you know

You know that a number is divisible by 6 if it is divisible by both 3 and 2. So why isn’t a number divisible by 8 if it is divisible by both 4 and 2?

What characteristic do the numbers 8, 10, 15, 26, and 33 have that the numbers 5, 9, 16, 18, and 24 don’t
have? (Hint: List the factors of the numbers.)



Give two more numbers that have this characteristic.

Do you think that the formula p = 6n + 1 where n is a whole number, will produce a prime number more than 50% of the time?


Give evidence to support your conclusion.

Answer 1

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Answer 2

1078=2 * 7 * 7 * 11

3315=3 * 5 * 13 * 17

This two numers haven't common divisors.
Thats why 1,078 and 3,315 are relatively prime

Answer 3

57 percent of 500