Prime number, Composite number, Multiples, Factors ：練習問題

Which of the following statements about the number 1 is true?

A number is a multiple of \(6\) and a factor of \(48\). Which of the following could be the value of this number?

Two different prime numbers are both factors of a certain number \(Y\). If the sum of these two prime numbers is \(12\), and \(Y\) is the smallest possible common multiple of both numbers, what is the value of \(Y\)?

Which of the following numbers is a factor of \(42\)?

A number is a multiple of \(9\) and is between \(60\) and \(80\). If this number is an even number, what is the value of the number?

Which of the following numbers has only two factors, 1 and itself?

What is the greatest two-digit number that is a multiple of both $$3$$ and $$7$$? Is this number prime or composite?

A composite number C is less than $$20$$. Its prime factors are exactly two distinct prime numbers. The sum of these two distinct prime numbers is $$8$$.

First, list all the factors of C. Then, identify which of these factors are composite numbers. Finally, what is the product of all the composite factors of C?

A baker prepares batches of muffins. Each batch contains $$6$$ muffins.

a) List the first five multiples of $$6$$.

b) If the baker made $$4$$ batches, how many muffins did he make in total? Is this total number a prime or composite number? Explain your answer.

A teacher has 24 blue pens and 36 red pens. She wants to pack them into bags such that each bag has the same number of blue pens and the same number of red pens, with no pens left over.
a) Find all the common factors of 24 and 36.
b) What is the Highest Common Factor (H.C.F.) of 24 and 36?
c) What is the maximum number of bags the teacher can pack?
d) How many blue pens and how many red pens will be in each bag if she packs the maximum number of bags?