Identify the Prime Factor in this ??5 Number

Prime Factorization with Divisibility Rules

I am a three-digit number ??5 ??5

Which prime factor will surely appear among my first factors?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Which factor definitely appears in the prime factors of the number?
00:03 Every number ending in digit 5 is divisible by 5
00:06 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

I am a three-digit number ??5 ??5

Which prime factor will surely appear among my first factors?

2

Step-by-step solution

We need to determine which prime factor is guaranteed for the number's appearance. The number is a three-digit number ending with 5, indicated as ??5 ??5 .

Based on divisibility rules, a number ending in 5 is divisible by 5. Therefore, 5 must be a factor.

Thus, the prime factor that surely appears in the factorization of any number ending in 5 is 5 5 .

Therefore, the solution to the problem is 5 5 .

3

Final Answer

5 5

Key Points to Remember

Essential concepts to master this topic
  • Divisibility Rule: Numbers ending in 5 are always divisible by 5
  • Technique: Any three-digit number like 125, 335, 995 contains prime factor 5
  • Check: Verify that 5 divides evenly into any number ending in 5 ✓

Common Mistakes

Avoid these frequent errors
  • Looking for other prime factors first
    Don't check if 3, 7, or other primes divide the number first = missing the guaranteed factor! You might waste time testing various primes when the last digit already tells you the answer. Always apply divisibility rules based on the number's ending digit first.

Practice Quiz

Test your knowledge with interactive questions

Write all the factors of the following number: \( 6 \)

FAQ

Everything you need to know about this question

Why is 5 guaranteed to be a factor for any number ending in 5?

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This comes from the divisibility rule for 5: any number ending in 0 or 5 is divisible by 5. Since your number ends in 5, it must have 5 as a factor, regardless of what the first two digits are!

Could there be other prime factors too?

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Absolutely! The number could have other prime factors like 3, 7, 11, etc. But the question asks which prime factor will surely appear, meaning it's guaranteed for every possible ??5 ??5 number.

What if the number was something like 115 or 225?

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Perfect examples! 115 = 5 × 23 and 225 = 5² × 3². Both contain 5 as a prime factor, proving that any three-digit number ending in 5 will have 5 in its prime factorization.

How do I remember divisibility rules?

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For 5, it's simple: if the last digit is 0 or 5, the number is divisible by 5. For 2, the last digit must be even. For 3, add all digits - if that sum is divisible by 3, so is the original number!

Is 5 always a prime factor, or could it appear multiple times?

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Great question! 5 could appear multiple times in the factorization. For example, 125 = 5³, so 5 appears three times. But it will appear at least once in any number ending in 5.

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