Number Theory I Junior Math Circles - University Of Waterloo Faculty Of Mathematics Worksheet With Answers Page 7
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1
2
3
4
5
6
77
Answers
1. The possibilities are: 1 group of 36 students, 2 groups of 18 students, 3 groups
of 12 students, 4 groups of 9 students, 6 groups of 6 students, 9 groups of 4
students, 12 groups of 3 students, 18 groups of 2 students and 36 groups of 1
student.
2. 211
3.
100
100
4
25
10
10
5
2
5
5
2
2
2
5
4. The different possible dimensions are:
1cm
1 cm
1925 cm
1cm
35 cm
55cm
1 cm
5 cm
385 cm
5 cm
5 cm
77 cm
1cm
7 cm
275 cm
5 cm
7 cm
55 cm
1 cm
11 cm
175 cm
5 cm
11 cm
35 cm
1 cm
25 cm
77 cm
7 cm
11 cm
25 cm
5. 9
6. 20 or 80 - The number could be 4320 or 4380.
7. (a) Yes, by definition, if a number is divisible by 2 and by 3 then it is divisible
by 6.
(b) No, for example, in the exercise in the lesson above, 1420 is divisible by 4
and by 2 but it is not divisible by 8.
8. 15.
9. 75. The three divisors are 72, 2, and 1.
10. abcdef = 324561
11. 42
12. x = 15 and y = 37, so x + y = 52.
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