The number of factors of a prime number is ____.
2
Step 1: What is a factor?
A factor of a number is a whole number that divides it exactly (no remainder).
We say \(a\) is a factor of \(n\) if:
\(n \div a\) leaves remainder \(0\).
Step 2: What is a prime number?
A prime number is a number greater than 1 that has only two different factors.
Those two factors are always:
\(1\) and the number itself.
Step 3: Example (Prime)
Take \(7\):
\(7 \div 1 = 7\) → exact, so \(1\) is a factor.
\(7 \div 7 = 1\) → exact, so \(7\) is a factor.
Try other numbers between 1 and 7:
\(7 \div 2\) is not exact,
\(7 \div 3\) is not exact,
… so there are no more factors.
Factors of \(7\): \(1, 7\) → total factors = \(2\).
Step 4: Compare (Not prime)
Take \(6\):
\(6 \div 1 = 6\), \(6 \div 2 = 3\), \(6 \div 3 = 2\), \(6 \div 6 = 1\).
Factors of \(6\): \(1, 2, 3, 6\) → total factors = \(4\) (so \(6\) is not prime).
Conclusion:
Every prime number has exactly two factors: \(1\) and itself.