Finding All Factors: A Look at the Number 6

Factor Identification with Prime Factorization

Write all the factors of the following number: 6 6

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Step-by-step video solution

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00:00 Find all prime factors of the number
00:03 The ones digit is 6, therefore 2 is definitely a prime factor
00:07 Divide by 2, and continue with the result to find the factors
00:10 And the result is a prime number, therefore it's a factor by itself
00:13 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
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Understand the problem

Write all the factors of the following number: 6 6

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Step-by-step solution

To determine the factors of the number 6 6 , we will follow these steps:

  • Step 1: Begin by checking each number starting from 1 1 up to 6 6 to see if it divides 6 6 evenly.

  • Step 2: Check 1 1 . Since 1×6=6 1 \times 6 = 6 , 1 1 is a factor.

  • Step 3: Check 2 2 . Since 2×3=6 2 \times 3 = 6 , 2 2 is a factor.

  • Step 4: Check 3 3 . Since 3×2=6 3 \times 2 = 6 , 3 3 is a factor.

  • Step 5: Check 4 4 . Since 6 6 is not evenly divisible by 4 4 , 4 4 is not a factor.

  • Step 6: Check 5 5 . Since 6 6 is not evenly divisible by 5 5 , 5 5 is not a factor.

  • Step 7: Finally, check 6 6 . Since 6×1=6 6 \times 1 = 6 , 6 6 is a factor.

All possible whole number products (pairs) that result in 6 6 are 1×6 1 \times 6 , 2×3 2 \times 3 , 3×2 3 \times 2 , and 6×1 6 \times 1 .

However, when checking for unique prime factors as a particular approach in factors identification, 6 6 breaks down into prime factors of 2 2 and 3 3 .

Therefore, the primary distinct prime factors of 6 6 are 2 2 and 3 3 .

This correlates with choice 3:

  • Choice 3 3 : 2,3 2,3 , which matches our factors.

Thus, the answer is correctly represented as the distinct prime factors 2,3 2, 3 in the context of the problem requirements.

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Final Answer

2,3 2,3

Key Points to Remember

Essential concepts to master this topic
  • Factor Definition: Numbers that divide evenly into a given number
  • Technique: Test divisibility: 6÷2=3 6 ÷ 2 = 3 and 6÷3=2 6 ÷ 3 = 2
  • Check: Multiply factors together: 2×3=6 2 × 3 = 6 confirms correct factors ✓

Common Mistakes

Avoid these frequent errors
  • Listing all factors instead of prime factors only
    Don't list all factors like 1, 2, 3, 6 when asked for prime factors = includes composite numbers! The question asks specifically for prime factors, which are the building blocks. Always identify prime factors only: numbers greater than 1 with exactly two factors.

Practice Quiz

Test your knowledge with interactive questions

Write all the factors of the following number: \( 9 \)

FAQ

Everything you need to know about this question

What's the difference between factors and prime factors?

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Factors are all numbers that divide evenly into 6: {1, 2, 3, 6}. Prime factors are only the prime numbers that multiply to make 6: {2, 3}. Prime factors are the building blocks!

Why isn't 1 considered a prime factor?

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The number 1 is not prime because prime numbers must have exactly two factors: 1 and themselves. Since 1 only has one factor (itself), it's neither prime nor composite.

How do I find prime factors of larger numbers?

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Start with the smallest prime number (2) and divide repeatedly. Then try 3, 5, 7, etc. For example: 12=2×2×3 12 = 2 × 2 × 3 , so prime factors are 2 and 3.

Can I list the same prime factor twice?

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When finding distinct prime factors, list each prime only once. For 6, write {2, 3}, not {2, 3, 2}. If the question asks for prime factorization, then you'd write 21×31 2^1 × 3^1 .

What if a number is already prime?

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If the number itself is prime (like 7 or 11), then it only has one prime factor: itself. For example, the only prime factor of 7 is 7.

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