Find the number of factors of 500

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

500 has exactly 12 factors. Reason in simple words: To find the number of factors (divisors) of a number, first write its prime factorization. Then add 1 to each exponent and multiply those results. For 500, the prime factorization is 2² × 5³. So the count of factors is (2+1)×(3+1) = 3×4 = 12.

Step-by-step method

Prime factorize 500: 500 = 5 × 100 = 5 × (4 × 25) = 2² × 5³.
Use divisor count formula: If n = p^a × q^b, then total divisors = (a+1)(b+1).
Apply: (2+1)(3+1) = 3×4 = 12 divisors.

All factors of 500

The 12 positive factors are: 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500.

Quick checks and tips

Even? Yes → divisible by 2.
Ends with two zeros? Yes → divisible by 4 and 25, and by 100.
Ends in 0? Yes → divisible by 5 and 10.

Pattern	What it means
Ends with 0	Divisible by 2 and 5
Ends with 00	Divisible by 4, 25, and 100
Sum of digits divisible by 3	Divisible by 3 (not the case for 500)

Watch 3-min video & get full concept clarity