Difference between revisions of "2005 iTest Problems/Problem 4"
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| − | Taking one factor of <math>2005</math> as a base, the other is split into <math>5 ^1 \ | + | ==Problem== |
| + | How many multiples of <math>2005</math> are factors of <math>(2005)^2</math>? | ||
| + | |||
| + | ==Solution 1== | ||
| + | Taking one factor of <math>2005</math> as a base, the other is split into <math>5 ^1 \cdot{ 401 ^1} = 2005</math>. This means <math>2005</math> has <math>(1 + 1)\cdot{(1 + 1)} = 4</math> divisors. Each of these divisors represents a multiple of <math>2005</math>, meaning the answer is <math>\boxed{4}</math>. | ||
| + | |||
| + | ==See Also== | ||
| + | {{iTest box|year=2005|num-b=3|num-a=5}} | ||
Revision as of 17:00, 13 October 2025
Problem
How many multiples of 
are factors of 
?
Solution 1
Taking one factor of as a base, the other is split into 
. This means has 
divisors. Each of these divisors represents a multiple of , meaning the answer is 
.
See Also
| 2005 iTest (Problems, Answer Key) | ||
| Preceded by: Problem 3 |
Followed by: Problem 5 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 • 51 • 52 • 53 • 54 • 55 • 56 • 57 • 58 • 59 • 60 • TB1 • TB2 • TB3 • TB4 | ||
