How many 4 digit positive integers have the ones digit a multiple of 1, the tens digit a multiple of 2, the hundreds digit a multiple of 3 and the thousands digit a multiple of 4?

(2)(4)(5)(10)=400

400 To find the number of 4-digit positive integers with specific conditions, we can break down the problem into four separate conditions for each digit place.

Condition 1: The ones digit must be a multiple of 1.
Since any integer is divisible by 1, there are 10 choices for the ones digit.

Condition 2: The tens digit must be a multiple of 2.
Since the ones digit is already determined as a multiple of 1, there are only 5 choices left for the tens digit (0, 2, 4, 6, or 8).

Condition 3: The hundreds digit must be a multiple of 3.
Considering the previous two conditions, there are only 3 choices left for the hundreds digit (0, 3, or 6).

Condition 4: The thousands digit must be a multiple of 4.
Again, considering the previous three conditions, there are only 2 choices left for the thousands digit (0 or 4).

To find the total number of 4-digit positive integers that satisfy all the given conditions, we multiply the number of choices at each digit place: 10 choices for the ones digit, 5 choices for the tens digit, 3 choices for the hundreds digit, and 2 choices for the thousands digit.

Total number of 4-digit positive integers = 10 × 5 × 3 × 2 = 300.

Therefore, there are 300 4-digit positive integers that have the ones digit a multiple of 1, the tens digit a multiple of 2, the hundreds digit a multiple of 3, and the thousands digit a multiple of 4.