Identify Factors of the Prime Number 7

Q: What's the difference between factors and prime factors?

Factors are ALL numbers that divide evenly into your number. Prime factors are only the prime numbers used to build your number through multiplication. For 7, the factors are 1 and 7, but 7 has no prime factors since it's already prime!

Q: Why does 7 only have two factors?

Because 7 is a prime number! Prime numbers can only be divided evenly by 1 and themselves. Try dividing 7 by 2, 3, 4, 5, or 6 - you'll always get decimals, not whole numbers.

Q: How do I check if a number divides evenly?

Divide the larger number by the smaller one. If you get a whole number (no decimal), then it's a factor. For example: $ \frac{7}{2} = 3.5 $ has a decimal, so 2 is not a factor.

Q: Can a prime number have more than 2 factors?

No, never! By definition, a prime number has exactly 2 factors: 1 and itself. If it had more factors, it wouldn't be prime anymore - it would be composite.

Prime Number Factors with Single Digit Numbers

Write all the factors of the following number: $7$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find all the prime factors of the number

00:03 The ones digit is 7, therefore 2 is definitely a prime factor

00:09 Let's divide by factors and check

00:14 The number itself is prime, so it's only divisible by itself and 1

00:18 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Write all the factors of the following number: $7$

Step-by-step solution

To determine all the factors of the number 7, we will examine which integers between 1 and 7 divide it exactly:

Check 1: Since $\frac{7}{1} = 7$ , 1 is a factor.
Check 2: $\frac{7}{2} = 3.5$ , which is not an integer, so 2 is not a factor.
Check 3: $\frac{7}{3} \approx 2.333$ , which is not an integer, so 3 is not a factor.
Check 4: $\frac{7}{4} = 1.75$ , which is not an integer, so 4 is not a factor.
Check 5: $\frac{7}{5} = 1.4$ , which is not an integer, so 5 is not a factor.
Check 6: $\frac{7}{6} \approx 1.167$ , which is not an integer, so 6 is not a factor.
Check 7: Since $\frac{7}{7} = 1$ , 7 is a factor.

Therefore, the factors of 7 are $1$ and $7$ .

These results correspond to choice 1: $1, 7$ .

Final Answer

No prime factors

Key Points to Remember

Essential concepts to master this topic

Prime Definition: A prime number has exactly two factors: 1 and itself
Factor Check: Divide 7 by each number from 1 to 7
Verification: Only 7÷1=7 and 7÷7=1 give whole number results ✓

Common Mistakes

Avoid these frequent errors

Confusing factors with prime factorization
Don't list prime factors like 2, 3 when asked for all factors = missing the question entirely! Prime factorization breaks numbers into prime components, but factors are all numbers that divide evenly. Always find every number that divides the given number exactly.

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?

Factors are ALL numbers that divide evenly into your number. Prime factors are only the prime numbers used to build your number through multiplication. For 7, the factors are 1 and 7, but 7 has no prime factors since it's already prime!

Why does 7 only have two factors?

Because 7 is a prime number! Prime numbers can only be divided evenly by 1 and themselves. Try dividing 7 by 2, 3, 4, 5, or 6 - you'll always get decimals, not whole numbers.

How do I check if a number divides evenly?

Divide the larger number by the smaller one. If you get a whole number (no decimal), then it's a factor. For example: $\frac{7}{2} = 3.5$ has a decimal, so 2 is not a factor.

Is 1 always a factor of every number?

Yes! Every positive whole number can be divided by 1 exactly. So 1 is a universal factor - it's a factor of every positive integer.

Can a prime number have more than 2 factors?

No, never! By definition, a prime number has exactly 2 factors: 1 and itself. If it had more factors, it wouldn't be prime anymore - it would be composite.

What if I can't remember which numbers are prime?

Just test each number systematically! Divide your number by every integer from 1 up to itself. Count how many give you whole number results - if it's exactly 2, you have a prime!

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