Is 21 Divisible by 4? A Number Theory Exploration

Divisibility Rules with Two-Digit Numbers

Is the number 21 divisible by 4?

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Step-by-step video solution

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00:00 Is the number divisible by 4?
00:03 Multiply the tens digit by 2, and add the ones digit to it
00:06 If this number is divisible by 4, then the number itself is divisible by 4
00:13 The number is not divisible by 4
00:16 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

Is the number 21 divisible by 4?

2

Step-by-step solution

To determine if 21 is divisible by 4, we apply the divisibility rule for 4.

The rule states that a number is divisible by 4 if the number formed by its last two digits is divisible by 4. Since 21 only has two digits, we consider the entire number.

Checking if 21 is divisible by 4:
We calculate 21÷4 21 \div 4 .

The quotient is 5 with a remainder of 1, since 4×5=20 4 \times 5 = 20 and 2120=1 21 - 20 = 1 .

Since there is a remainder, 21 is not divisible by 4. According to the divisibility rule, if there is any remainder other than zero, the number is not divisible.

Therefore, the correct conclusion is that 21 is not divisible by 4, and thus the number 21 is not divisible by 4.

3

Final Answer

No

Key Points to Remember

Essential concepts to master this topic
  • Rule: A number is divisible by 4 if remainder equals zero
  • Technique: Calculate 21÷4=5 remainder 1 21 \div 4 = 5 \text{ remainder } 1
  • Check: Verify by multiplication: 4×5+1=21 4 \times 5 + 1 = 21

Common Mistakes

Avoid these frequent errors
  • Confusing quotient with divisibility
    Don't think 21 is divisible by 4 just because 21 ÷ 4 = 5.25! Getting a decimal or remainder means NOT divisible. Always check if the remainder is exactly zero for true divisibility.

Practice Quiz

Test your knowledge with interactive questions

Is the number 43 divisible by 4?

FAQ

Everything you need to know about this question

What does it mean for a number to be divisible by another?

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A number is divisible by another if it divides evenly with no remainder. For example, 20 ÷ 4 = 5 exactly, so 20 is divisible by 4.

Can I use the divisibility rule for 4 with any number?

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Yes! For numbers with more than 2 digits, check if the last two digits are divisible by 4. For 21, we check the whole number since it only has 2 digits.

Why does 21 ÷ 4 = 5.25 mean it's not divisible?

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The decimal .25 shows there's a remainder! When we get 5.25, it means 5 whole groups plus a leftover piece. True divisibility means no leftover pieces.

How can I quickly check if 21 is divisible by 4 without a calculator?

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Use mental math: 4×5=20 4 \times 5 = 20 , and 21 - 20 = 1. Since there's a remainder of 1, 21 is not divisible by 4.

What's the difference between quotient and remainder?

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The quotient is how many complete groups you can make (5 in this case). The remainder is what's left over (1 here). For divisibility, the remainder must be 0!

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