What Is the Prime Factorization of 1,001?
1,001 = 7 × 11 × 13. Every number in that product is prime, so it cannot be broken down any further. The prime factors of 1,001 are 7, 11, 13.
Division Ladder for 1,001
Divide by the smallest prime that goes in, write the answer, and repeat until you reach 1.
- 1,001 ÷ 7 = 143
- 143 ÷ 11 = 13
- 13 ÷ 13 = 1
The numbers in bold are the prime factors: 7 × 11 × 13.
Write It with Exponents
- 7 appears 1 time, written 7
- 11 appears 1 time, written 11
- 13 appears 1 time, written 13
Put together: 1,001 = 7 × 11 × 13.
Check by Multiplying Back
7 × 11 × 13 = 1,001. It matches the number we started with, so the factorization is right.
Count the Factors of 1,001
Add 1 to each exponent and multiply: (1 + 1) × (1 + 1) × (1 + 1) = 8. So 1,001 has 8 factors:
1, 7, 11, 13, 77, 91, 143, 1,001
See them paired up on the factors of 1,001 page.
Prime or composite?
1,001 is composite, because it has more than two factors. Try another number in the Prime Factorization Calculator.