Which Of The Following Numbers Are Multiples Of 4

Understanding Multiples of 4: A Simple Guide with Examples

Identifying multiples of 4 is a fundamental skill in arithmetic that builds a bridge between basic counting and more advanced number theory. At its core, a multiple of 4 is any number that can be expressed as 4 multiplied by an integer (a whole number). This means when you divide a multiple of 4 by 4, the result is always a whole number with no remainder. This concept is not just an abstract math idea; it underpins patterns in time, money, measurements, and computer science. Whether you're a student solidifying foundational knowledge or an adult refreshing a useful skill, mastering this rule provides a quick mental tool for solving countless everyday problems. This guide will walk you through the precise, reliable method to determine if any given number belongs to the 4-times table, using clear examples and explaining the logic behind the famous divisibility rule.

What Exactly Is a Multiple?

Before applying the rule, we must define our terms precisely. A multiple of a number is the product you get when you multiply that number by any integer. For the number 4, its multiples form an infinite sequence: 4, 8, 12, 16, 20, 24, 28, 32, and so on, continuing forever in both positive and negative directions (…, -8, -4, 0, 4, 8, …). The number 0 is also a multiple of 4 because 4 × 0 = 0. When we ask "which of the following numbers are multiples of 4?" we are essentially asking which numbers fit perfectly into this sequence without any gaps or leftovers. The key test is divisibility: if a number can be divided by 4 with a remainder of zero, it is a multiple.

The Golden Rule: The Divisibility Test for 4

You do not need to perform long division for every number. Mathematicians have discovered a swift shortcut, known as the divisibility rule for 4. This rule states:

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

This works because 100 is itself a multiple of 4 (100 ÷ 4 = 25). Any number larger than 100 can be broken down into a multiple of 100 plus its last two digits. Since any multiple of 100 is automatically a multiple of 4, the entire number's divisibility hinges solely on that final two-digit piece. For example, in the number 1,236, we only need to check if 36 is divisible by 4. Because 36 ÷ 4 = 9, we know 1,236 is also a multiple of 4.

This rule is incredibly efficient, turning a potentially complex division problem into a simple check of a two-digit number that you can often recognize instantly.

Step-by-Step Method to Identify Multiples of 4

Let's apply this rule systematically. Imagine we are given the following list of numbers to evaluate: 12, 18, 24, 37, 40, 55, 68, 81, 92, 100

Here is the exact process you would follow for each one:

1. Isolate the last two digits. For single-digit numbers like 4 or 8, you can consider them as 04 and 08, but typically, if a number has fewer than two digits, you just check the number itself. For our list:

   • 12 → last two digits: 12
   • 18 → last two digits: 18
   • 24 → last two digits: 24
   • 37 → last two digits: 37
   • 40 → last two digits: 40
   • 55 → last two digits: 55
   • 68 → last two digits: 68
   • 81 → last two digits: 81
   • 92 → last two digits: 92
   • 100 → last two digits: 00 (which is 0)

2. Determine if this two-digit number is divisible by 4. You can use your knowledge of the 4-times table, perform simple mental division, or check if it's an even number that, when halved, results in an even number (a secondary check).

   • 12 ÷ 4 = 3 → Yes, multiple of 4.
   • 18 ÷ 4 = 4.5 → No, not a multiple of 4.
   • 24 ÷ 4 = 6 → Yes, multiple of 4.
   • 37 ÷ 4 = 9.25 → No, not a multiple of 4.
   • 40 ÷ 4 = 10 → Yes, multiple of 4.
   • 55 ÷ 4 = 13.75 → No, not a multiple of 4.
   • 68 ÷ 4 = 17 → Yes, multiple of 4.
   • 81 ÷ 4 = 20.25 → No, not a multiple of 4.
   • 92 ÷ 4 = 23 → Yes, multiple of 4.
   • 00 (0) ÷ 4