Careful Counting
Divisibility, GCF, LCM
Fiendish Factors
Surprise Me!
200
We have a group of 3 different dogs and 4 different cats. How many ways are there to arrange these animals in a straight line such that all the dogs are all together and all the cats are all together?
288
200
A679B is a 5-digit integer which is divisible by 72. What is the value of A + B?
5
200
Let N = 28 x 34 x 7. How many odd factors does N have?
10
200
A jar of marbles contains: 6 Red, 3 White, 2 Green, and 1 Black. What is the smallest number of marbles you need to remove from the jar (blindfolded) to guarantee you end up with at least 3 marbles of the same color?
8
400
How many 4-digit integers have all their digits of the same parity; i.e. all even or all odd?
1125
400
Given that GCF(a, b) = 10 and GCF (b, c) = 7, what is the smallest possible value of a x b x c?
4900
400
How many perfect cube factors does the number 1,000,000,000 have?
16
400
A 28 mile road is split into three unequal parts. The distance between the centers of the first and third parts is 16 miles. Find the length, in miles, of the middle portion of the road.
4
600
How many even integers are there between 200 and 700 whose digits are all different, and the digits come from the list 1, 2, 3, 5, 7, 8?
20
600
Find GCF(10!, 1010).
6400
600
Find the sum of all the factors of 1,200 which have exactly 8 factors of their own.
94
600
How many squares (of any size and in any orientation) are in the picture below?
31