2026 AMC 8 Problem 16: Solution

Work through 2026 AMC 8 Problem 16 on divisibility with a written solution, hints, and a visual explanation.

Number TheoryLevel 4 · Challenge

Consider all positive four-digit integers consisting of only even digits. What fraction of these integers are divisible by 4?

  • A. 1/4
  • B. 2/5
  • C. 1/2
  • D. 3/5
  • E. 3/4
Hints
  1. Recall the rule for divisibility by 4: only the last two digits of a number matter.
  2. Since every digit must be even, think about whether the tens digit can ever affect the outcome.
  3. With the tens digit always even, test each of the 5 possible ones digits (0, 2, 4, 6, 8) to see which ones make the last two digits a multiple of 4.
Read the step-by-step solution

Answer: D · 3/5

  1. Identify the key divisibility rule

    A number is divisible by 4 if its last two digits form a number divisible by 4. Since all digits must be even (0, 2, 4, 6, 8), the first two digits don't affect divisibility by 4.

  2. Check the ones digit

    Since the tens digit is always even, divisibility by 4 depends only on the ones digit. Of the 5 even digits {0, 2, 4, 6, 8}, exactly 3 (namely 0, 4, 8) make the last two digits divisible by 4.

    3/5

Loading practice tools…