Three digit numbers by one digit numbers

Try to do these problems without pencil and paper.

1. What is 200 / 5 ?

2. What is 888 / 4 ?

3. What is 180 / 9 ?

4. What is 633 / 3 ?

5. What is 248 / 8 ?

Three digit numbers by one digit numbers

Try to do these problems without pencil and paper.

1. What is 200 / 5 ?

2. What is 888 / 4 ?

3. What is 180 / 9 ?

4. What is 633 / 3 ?

5. What is 248 / 8 ?

Three digit numbers by two digit numbers

Try to work out these divisions without pencil and paper.

1. What is 360 / 12 ?

2. What is 121 / 11 ?

3. What is 200 / 40 ?

4. What is 560 / 70 ?

5. What is 560 / 14 ?

Each of these problems involves division *somewhere*. Solve each problem.

1. Effie runs 8 miles in 2 hours. What is her average speed?

2. Six friends play hockey together after school. Their ages are 9, 12, 10, 11, 15, and 9. What is the average age of people on the team?

3. A group of fourteen squirrels has found a pile of 42 nuts. They decide to share the nuts equally among themselves. How many nuts does each squirrel get?

4. What is the probability that you will roll a 3 or a 5 on a six-sided die ?

5. The area of Harry’s rectangular swimming pool is 200 square meters. The width of the pool is 8 meters. What is the length of the pool?

Two digit numbers by two digit numbers.

1. What is 24 / 12?

2. What is 36 / 18?

3. What is 45 / 15?

4. What is 80 / 10?

5. What is 28 / 14?

Two digit numbers by one digit numbers.

1. What is 24 / 6?

2. What is 36 / 9?

3. What is 48 / 8?

4. What is 63 / 7?

5. What is 88 / 8?

Answers

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1. The prime decomposition of a number is 2 x 11. What are all possible factors of the number?

2. The prime decomposition of a number is 2 x 3 x 3 x 5. What are all possible factors of the number?

3. The prime decomposition of a number is 2 x 3 x 5 x 7. Is this number divisible by 21?

4. The prime decomposition of a number is 2 x 2 x 5 x 5 x 5. How many zeros are at the right end of the number (in other words, how many multiples of 10 can go into the number)?

5. Sally has opens her book. The product of the two open page numbers is 210. What are the page numbers?

Prime Decomposition

Positive whole numbers can be written as products of prime numbers, in a unique way from smallest prime factor to largest prime factor.

1. What are the prime factors of 6?

2. What are the prime factors of 42?

3. What are the prime factors of 32?

4. Write the number 45 as a product of primes.

5. Write the number 84 as a product of primes.

How Many Prime Numbers Are There?

1. How many prime numbers are less than 10?

2. How many prime numbers are between 10 and 20?

3. How many prime numbers are between 20 and 30?

4. How many prime numbers are between 30 and 40?

5. In a group of ten consecutive numbers > 10, what is the maximum number of primes there could be? (Hint: how many of the ten numbers MUST be even? Knock those out. What other multiples can you eliminate?) It might help to write the numbers down as a list and cross out the possibilities.

How can you tell if a number is prime?

A prime number has only two factors.

1. Which of the following numbers is divisible by 2 (and definitely not prime)?

17, 26, 101, 924, 1000000, 39

2. Which of the following numbers is divisible by 3 (and definitely not prime)?

16, 51, 39, 243, 117, 2014, 2016

3. Which of the following numbers is divisible by 9 (and definitely not prime)?

16, 51, 39, 72, 243, 117, 2010, 2014, 2016

4. Which of the following numbers is divisible by 7?

18, 28, 43, 45, 49, 52, 63, 72, 87, 91, 98

5. Which of the following numbers is divisible by 15?

16, 51, 39, 72, 243, 117, 2010, 2014, 2016

Answers

A prime number has precisely two distinct (different) factors: itself and 1.

The number 1 is not prime. It has only one factor.

1. How many even prime numbers are there?

2. List all the prime numbers between 10 and 20.

3. What is the name for a whole number > 1 that is not prime?

4. List three consecutive prime numbers.

5. Is it true that the sum of two prime numbers is a prime number?