Math Problem Statement

Here are four digits: 0, 1, 2, 4. Write a different digit in each box so that each number is divisible by 4: 28_, 430_, 55_, 1_6.

Solution

To solve this problem:

Instructions:

We need to fill the boxes with digits (from 0, 1, 2, and 4) so that:

  1. Each number is divisible by 4.
  2. Each digit must be used only once.

Step-by-step solution:

Key rule for divisibility by 4:

  • A number is divisible by 4 if the number formed by its last two digits is divisible by 4.

Solutions for each number:

  1. 28_:

    • The number ends in 28. For the third digit, we choose a number from the available set {0, 1, 2, 4}. If 2 is used, the full number becomes 280, which is divisible by 4.
  2. 430_:

    • This number ends in 30_. For divisibility by 4, we use 4, forming the number 4304, which is divisible by 4.

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Math Problem Analysis

Mathematical Concepts

Divisibility Rules
Number Properties

Formulas

A number is divisible by 4 if its last two digits are divisible by 4.

Theorems

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Suitable Grade Level

Grades 5-7