Download Divisibility Rules Ex: What is the remainder when 1,427 is divided by

Divisibility Rules
Ex: What is the remainder when 1,427 is divided by 3?
1. 124,232,22B has 33 as a factor. What could B be?
2. A=?25? is divisible by 12. What is the smallest possible value of A?
3. What is the largest 4-digit multiple of 8 which has 3, 5, and 7 among its digits?
The one’s digit
Ex: What is the last digit of:
1. Is 1238 a perfect square? Why or why not?
2. What is the units digit of 7100?
3. The Fibonacci numbers are defined so that F1=1, F2=1 and Fn=Fn-1+Fn-2. What is
the remainder of F60 divided by 10?
Factoring, Divisibility and Number Stuff
Ex: How many factors does 96 have and what is their sum? How many are even?
Ex: N has a remainder of 3 when you divide it by 4, 5, 6 and 8. N is the second smallest
number that had this property. What is N?
1. What is the largest prime factor of 360?
2. How many divisors are there of 1200?
3. How many odd factors does 120 have?
4. The integer x has 12 factors. The numbers 12 and 15 are factors of x. What is x?
General Questions
1. Alphonse writes the number “3” on the board. He then doubles it and writes the
new number beside his first number. Then he doubles his new number and
writes it on the board. He keeps doing this until he writes 100 numbers. What is
the one’s digit of the last number Alphonse writes?
2. Find the largest possible product of three positive primes which sum to 30.
3. The following multiplication uses all of the digits 0 to 9, once each. What is the
value of E?
A2B X C3 = 5DE01
4. At math club, everyone has to make teams. If the students make teams of 4,
there are 3 people left over. If they make teams of 5 there are 4 people left over
and teams of 6 would leave 5 over. How many students are there in math club?
5. Find the amount of positive numbers less than 1000 which do not have any
factors besides 1 in common with 1000.