Divisibility Dilemma: Does 4 Always Lead to 10?

Divisibility Rules with Multiple Number Conditions

If a number is divisible by 4, will it necessarily be divisible by 10?

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Step-by-step video solution

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00:00 Is a number divisible by 4 also divisible by 10?
00:03 Let's take an example of a number divisible by 4
00:09 We can see that this number is not divisible by 10
00:15 Therefore, not every number divisible by 4 is divisible by 10
00:18 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

If a number is divisible by 4, will it necessarily be divisible by 10?

2

Step-by-step solution

To determine if a number divisible by 4 must also be divisible by 10, we will apply the divisibility rules for both numbers.

The rule for divisibility by 4 is that the last two digits of the number form a number that is divisible by 4. For example, the number 8, or 112, or 236 is divisible by 4.

The rule for divisibility by 10 is that the number ends in 0. For example, the numbers 10, 30, 250, or 400 are divisible by 10.

Let's consider an example to illustrate the point. The number 8 is divisible by 4 because when divided by 4, it yields 2, which is an integer. However, 8 is not divisible by 10, as dividing 8 by 10 does not produce an integer. Therefore, a number that is divisible by 4 does not have to end in 0, which is required for divisibility by 10.

By analyzing these examples, we conclude that a number divisible by 4 is not necessarily divisible by 10. Specifically, divisibility by 4 depends on the last two digits, whereas divisibility by 10 depends on the last digit.

Therefore, the solution to the problem is that a number divisible by 4 will not necessarily be divisible by 10, making the answer No.

3

Final Answer

No.

Key Points to Remember

Essential concepts to master this topic
  • Rule: Divisibility by 4 requires last two digits divisible by 4
  • Technique: Check 8: divisible by 4 but not by 10
  • Check: Find counterexample: 12, 16, 20 work, but 8 doesn't ✓

Common Mistakes

Avoid these frequent errors
  • Assuming divisibility rules are connected
    Don't think divisible by 4 means divisible by 10 = wrong conclusion! These rules check different digit positions and have no direct relationship. Always test each divisibility rule independently using its own specific criteria.

Practice Quiz

Test your knowledge with interactive questions

Is the number 43 divisible by 4?

FAQ

Everything you need to know about this question

Why doesn't divisibility by 4 guarantee divisibility by 10?

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Because they check different things! Divisibility by 4 looks at the last two digits, while divisibility by 10 only cares if the number ends in 0. These are completely separate rules.

Can you give me more examples of numbers divisible by 4 but not 10?

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Sure! Try 12, 16, 24, 28, 32 - all divisible by 4 but none end in 0, so they're not divisible by 10. Only multiples of both 4 AND 10 work for both rules.

When would a number be divisible by both 4 and 10?

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When it's divisible by 20! Numbers like 20, 40, 60, 80 end in 0 (divisible by 10) and their last two digits (20, 40, 60, 80) are all divisible by 4.

How do I check if the last two digits are divisible by 4?

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Just divide those two digits by 4! For example, in 236, check if 36 ÷ 4 = 9 (yes!). If you get a whole number, then the original number is divisible by 4.

Is there a trick to remember divisibility by 10?

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Super easy! If it ends in 0, it's divisible by 10. That's it! Numbers like 30, 150, 2000 all work because they end in zero.

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