Number Theory I Junior Math Circles - University Of Waterloo Faculty Of Mathematics Worksheet With Answers

University of Waterloo

Centre for Education in

Faculty of Mathematics

Mathematics and Computing

Junior Math Circles

February 3, 2010

Number Theory I

Factors

Deﬁnition: A factor of a number is a whole number that divides evenly into the

other number. So, when you divide by the factor the remainder is zero.

Factors come in pairs. When you divide a number by one of its factors, the an-

swer or quotient is the paired factor.

Is 4 a factor of 36?

Yes, 36 divided by 4 gives us an answer of 9 with no remainder.

Is 3 a factor of 47?

No, 47 divided by 3 gives us an answer of 15 with a remainder of 2.

Exercise 1 State all the factors of the following numbers.

1) 50:

2) 15:

3) 13:

4) 36:

1, 2, 5, 10, 25, 50

1, 3, 5, 15

1, 13

1, 2, 3, 4, 6, 9, 12, 18, 36

Notice that 36 has an odd number of factors. Each factor still has a pair, but 6

pairs with itself, and is only listed once.

0 votes

Parent category: Education