Explore the Properties of 301: Prime Factor or Divisible?

Q: Why can't I just use a calculator to divide?

While calculators work, divisibility rules are faster and help you recognize patterns! For 301, seeing the last digit is 1 immediately tells you it's not divisible by 2, 4, 5, or 10.

Q: How do I remember the divisibility rule for 4?

Look at the last two digits only! For 301, the last two digits are '01' which equals 1. Since 1 ÷ 4 doesn't give a whole number, 301 isn't divisible by 4.

Divisibility Rules with Multiple Number Tests

The number 301...

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Step-by-step written solution

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Understand the problem

The number 301...

Step-by-step solution

To solve this problem, we'll apply divisibility rules to the number 301:

Divisibility by 2:
A number is divisible by 2 if its last digit is even. Since the last digit of 301 is 1, which is not even, 301 is not divisible by 2.
Divisibility by 4:
A number is divisible by 4 if the last two digits form a number divisible by 4. The last two digits of 301 are 01, which is 1. Since 1 is not divisible by 4, 301 is not divisible by 4.
Divisibility by 10:
A number is divisible by 10 if its last digit is 0. The last digit of 301 is 1, not 0, so 301 is not divisible by 10.

None of the divisibility rules for 2, 4, or 10 are satisfied by the number 301. Therefore, the correct answer is No answer is correct, corresponding to choice 4.

Final Answer

No answer is correct.

Key Points to Remember

Essential concepts to master this topic

Divisibility by 2: Last digit must be even (0, 2, 4, 6, 8)
Technique: For 301, last digit is 1 (odd), so not divisible by 2
Check: Test all rules systematically: 301 ÷ 2 = 150.5, confirms not divisible ✓

Common Mistakes

Avoid these frequent errors

Only checking if the division gives a whole number
Don't just divide 301 ÷ 2 = 150.5 and conclude it's not divisible! This wastes time and doesn't teach the pattern. Always apply the divisibility rule first: check if the last digit is even (it's 1, so odd = not divisible by 2).

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 can't I just use a calculator to divide?

While calculators work, divisibility rules are faster and help you recognize patterns! For 301, seeing the last digit is 1 immediately tells you it's not divisible by 2, 4, 5, or 10.

How do I remember the divisibility rule for 4?

Look at the last two digits only! For 301, the last two digits are '01' which equals 1. Since 1 ÷ 4 doesn't give a whole number, 301 isn't divisible by 4.

What if none of the given options work?

That's exactly what happened here! When you test all the divisibility rules and none of them work for 301, then 'No answer is correct' is the right choice.

Are there other numbers 301 might divide by?

Yes! You can factor 301 = 7 × 43, so 301 is divisible by 7 and 43. But the question only asked about 2, 4, and 10, and none of those work.

Why is the divisibility rule for 10 so simple?

Because 10 = 2 × 5, a number is divisible by 10 only if it's divisible by both 2 and 5. This happens only when the last digit is 0!

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