Which Of The Following Is Not A Multiple Of 12

Which of the following isnot a multiple of 12?

Introduction

When students encounter the phrase which of the following is not a multiple of 12, they are being asked to apply a simple yet powerful mathematical filter: divisibility by 12. This question appears frequently in standardized tests, classroom worksheets, and everyday problem‑solving scenarios. Which means understanding the underlying principles not only helps you answer a single multiple‑choice item but also builds a foundation for working with larger numbers, factoring, and algebraic expressions. In this article we will explore the concept of multiples of 12, outline a step‑by‑step method for identifying them, examine a sample multiple‑choice set, and provide practical tips to avoid common pitfalls.

Understanding Multiples of 12

A multiple of 12 is any number that can be expressed as 12 × n, where n is an integer (positive, negative, or zero). Because of this, the set of multiples of 12 begins:

• 0 (12 × 0)
• 12 (12 × 1)
• 24 (12 × 2)
• 36 (12 × 3)
• 48 (12 × 4) - 60 (12 × 5)

Because 12 = 3 × 4, a number must satisfy both divisibility by 3 and divisibility by 4 to be a multiple of 12. This dual condition is the key to quick mental checks.

Divisibility Rules to Remember

• Divisible by 3: The sum of the digits is a multiple of 3. - Divisible by 4: The last two digits form a number that is divisible by 4.

If a number meets both criteria, it is automatically a multiple of 12. This rule is far faster than performing long division for every candidate. ## How to Test If a Number Is a Multiple of 12

1. Check divisibility by 3

   • Add all digits together.
   • If the sum is 3, 6, 9, 12, etc., the number passes the first test.

2. Check divisibility by 4

   • Look at the last two digits only.
   • If those two digits form a number divisible by 4 (e.g., 00, 04, 08, 12, …, 96), the number passes the second test.

3. Combine the results

   • If the number satisfies both conditions, it is a multiple of 12.
   • If it fails either condition, it is not a multiple of 12.

Quick‑Reference List | Number | Sum of Digits | Last Two Digits | Divisible by 3? | Divisible by 4? | Multiple of 12? |

|--------|---------------|----------------|-----------------|-----------------|-----------------| | 84 | 8 + 4 = 12 | 84 | ✅ | ✅ | ✅ | | 150 | 1 + 5 + 0 = 6 | 50 | ✅ | ❌ | ❌ | | 216 | 2 + 1 + 6 = 9 | 16 | ✅ | ✅ | ✅ | | 300 | 3 + 0 + 0 = 3 | 00 | ✅ | ✅ | ✅ | | 350 | 3 + 5 + 0 = 8 | 50 | ❌ | ❌ | ❌ |

Common Multiple‑Choice Scenarios

In many tests, the question which of the following is not a multiple of 12 will present four or five options, only one of which fails the divisibility test. Let’s examine a typical set:

1. 144
2. 168
3. 200
4. 264

Step‑by‑Step Walkthrough

1. 144

   • Digit sum: 1 + 4 + 4 = 9 → divisible by 3.
   • Last two digits: 44 → 44 ÷ 4 = 11 → divisible by 4.
   • Result: multiple of 12.

2. 168

   Continue exploring with our guides on wordscapes daily puzzle october 31 2024 and you are at a local restaurant with colleagues.

   • Digit sum: 1 + 6 + 8 = 15 → divisible by 3.
   • Last two digits: 68 → 68 ÷ 4 = 17 → divisible by 4.
   • Result: multiple of 12.

3. 200

   • Digit sum: 2 + 0 + 0 = 2 → not divisible by 3.
   • Last two digits: 00 → divisible by 4, but the first test already fails. - Result: not a multiple of 12.

4. 264

   • Digit sum: 2 + 6 + 4 = 12 →

Completing the Example

4. 264

• Digit sum: 2 + 6 + 4 = 12 → divisible by 3.
• Last two digits: 64 → 64 ÷ 4 = 16 → divisible by 4.
• Result: 264 satisfies both conditions, so it is a multiple of 12.

With the four options now evaluated, the only number that fails the test is 200. In a multiple‑choice setting, the correct answer to “which of the following is not a multiple of 12?” would be 200.

A Few More Practice Sets

Set A

Answer: 123 is the sole non‑multiple.

Set B

Answer: 506 does not meet the divisibility‑by‑3 requirement, so it is not a multiple of 12.

Why the Two‑Step Test Works Every Time

The logic behind the rule is simple:

• Divisibility by 3 guarantees that the number can be expressed as 3 × k for some integer k.
• Divisibility by 4 guarantees that the same number can be expressed as 4 × m.

If a single integer satisfies both representations, it can be written as 3 × k = 4 × m, which means it is also 12 × n (where n = k/4 = m/3). As a result, the intersection of the two sets—multiples of 3 and multiples of 4—is exactly the set of multiples of 12. This intersection property is what makes the two‑step check both necessary and sufficient.

Quick Checklist for Exams

1. Add the digits. If the sum is 3, 6, 9, 12, 15, … the number passes the 3‑test.
2. Look at the final two digits. If they form 00, 04, 08, 12, 16, …, 96, the number passes the 4‑test.
3. If both ✔ appear, declare “multiple of 12.” Otherwise, it is not.

Keeping this three‑step mental script handy will let you sort through any list of candidates in seconds, even under timed conditions.

Conclusion

Identifying whether a number belongs to the 12‑times table is straightforward once you internalize the twin conditions of divisibility by 3 and by 4. Still, by summing the digits to verify the first condition and inspecting the last two digits for the second, you can instantly flag multiples of 12 without resorting to long division. Because of that, practicing with varied examples—like the sets illustrated above—builds confidence and speeds up problem‑solving on quizzes, standardized tests, or everyday calculations. Remember: a number is a multiple of 12 iff it satisfies both checks; failing either one guarantees it is not.