Number reference
173 explained.
173: one hundred seventy-three, prime; factors, prime factorization, roots, binary, hexadecimal, and digit properties.
Identity and representations
- Written form
- one hundred seventy-three
- Classification
- prime
- Factors
- 1, 173
- Prime factorization
- 173
- Square root
- 13.152946
- Cube root
- 5.572055
- Binary
- 10101101
- Octal
- 255
- Hexadecimal
- AD
- Roman numeral
- CLXXIII
- Digit sum
- 11
- Digital root
- 2
What makes 173 notable
- Prime. 173 is prime: it has exactly two divisors, 1 and itself, so it cannot be split into equal whole-number groups any other way.
173 in everyday use
One hundred seventy-three is a balanced prime, the exact average of its prime neighbours 167 and 179, so the three primes are evenly spaced six apart. It is also a Sophie Germain prime: 2 × 173 + 1 = 347 is prime. Such primes are named for the French mathematician who used them in early work on Fermat's Last Theorem and, long after, they became useful in generating safe primes for cryptography. As a Pythagorean prime it splits into two squares: 13² + 2² = 169 + 4.
Beyond those properties 173 has little everyday presence, though it shares a curious trait with 137: reversing its digits does not preserve primality, since 371 factors as 7 × 53. It is the 40th prime, marking the point where exactly forty primes have appeared among the first 173 counting numbers. Its digit sum is 11, and 173 sits at the start of the last stretch of the 100s, being followed by the primes 179, 181, 191, 193, 197, and 199.
Nearby numbers
How to read this page
Because 173 is prime, the factor list stops at 1 and 173 itself, so it cannot be shared into equal whole-number groups. That is also what makes it useful as a building block: every larger number with 173 in its prime factorisation inherits it from here.
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