I am not sure on this question. Can you help me. Question: How can you tell if 31/33 is already in its simplest form?

Question

I am not sure on this question. Can you help me. Question: How can you tell if 31/33 is already in its simplest form?

I wrote my answer to the following questions, can you tell if it is right?

Question: Can the Greatest Common Factor of 18 and 36 be greater than 18?

My Answer No, because 18 is the largest number that go into both 18 and 36 evenly.

Question: Can the Greatest Common Factor of 16 and 42 be less than 16?

My Answer: Yes, because 2 is the only number that can go into 16 and 42 evenly.

Answer 1

Your answers are correct. :-)

For your first question, can you think of any number that goes into 31 and 33?

Answer 2

the gcf can not be lower than 16

Answer 3

Sure, I'd be happy to help you with your questions!

For the first question, "How can you tell if 31/33 is already in its simplest form?", you can determine if a fraction is in its simplest form by finding the greatest common divisor (GCD) of the numerator and denominator. If the GCD is 1, then the fraction is already in its simplest form.

To find the GCD of 31 and 33, you can use different methods like prime factorization or the Euclidean algorithm. Let's use the Euclidean algorithm in this case.

Step 1: Divide the larger number (33) by the smaller number (31) to get the quotient and remainder.
33 ÷ 31 = 1 remainder 2

Step 2: Now, divide the previous divisor (31) by the remainder (2).
31 ÷ 2 = 15 remainder 1

Step 3: Repeat the process of dividing the previous divisor (2) by the remainder (1).
2 ÷ 1 = 2 remainder 0

At this point, the remainder becomes 0, and the GCD is the previous remainder, which is 1.

Since the GCD of 31 and 33 is 1, it means that 31/33 is already in its simplest form.

Now, let's review your answers for the second question, "Can the Greatest Common Factor of 18 and 36 be greater than 18?" and the third question, "Can the Greatest Common Factor of 16 and 42 be less than 16?"

Your answer for the second question is correct. The GCF (Greatest Common Factor) of 18 and 36 is indeed 18 because 18 is the largest number that can divide both 18 and 36 evenly.

However, your answer for the third question is incorrect. The GCF of 16 and 42 is not only 2. In this case, the GCF is actually 2 because 2 is the largest number that can divide both 16 and 42 evenly. So, the GCF cannot be less than 16.

I hope this helps clarify your questions! Let me know if you have any further inquiries.