Number reference
157 explained.
157: one hundred fifty-seven, prime; factors, prime factorization, roots, binary, hexadecimal, and digit properties.
Identity and representations
- Written form
- one hundred fifty-seven
- Classification
- prime
- Factors
- 1, 157
- Prime factorization
- 157
- Square root
- 12.529964
- Cube root
- 5.394691
- Binary
- 10011101
- Octal
- 235
- Hexadecimal
- 9D
- Roman numeral
- CLVII
- Digit sum
- 13
- Digital root
- 4
What makes 157 notable
- Prime. 157 is prime: it has exactly two divisors, 1 and itself, so it cannot be split into equal whole-number groups any other way.
157 in everyday use
One hundred fifty-seven has no famous role in daily life; it is one of the many primes that people meet mostly as a bus route, a page number, or a lock combination. Its interest is arithmetical. It is a balanced prime, sitting exactly halfway between the primes on either side of it, 151 and 163. It is also an emirp: read backwards it becomes 751, which is prime as well. Numbers with both properties are uncommon enough to be catalogued in reference lists of prime curiosities.
A more surprising fact concerns its square. 157² = 24,649 and 158² = 24,964, and the two squares use exactly the same five digits in a different order. Pairs of consecutive squares that are digit rearrangements of each other are rare; 13² = 169 and 14² = 196 form the smallest, and 157 and 158 the next. Adding the digits of 157 gives 13, another prime, and 157 is the 37th prime overall.
Nearby numbers
How to read this page
Because 157 is prime, the factor list stops at 1 and 157 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 157 in its prime factorisation inherits it from here.
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