Number analysis
7
The most commonly chosen "random" number when people are asked to pick one from 1 to 10.
The most commonly chosen "random" number when people are asked to pick one from 1 to 10.
The number itself
- Value
- 7
- Digits
- 1
- Digit sum
- 7
- Reversed
- 7
- Palindrome
- Yes
7
Digit sum repeated until one digit remains; equals n mod 9 (with 9 for multiples of 9).
Reads the same in both directions.
Parity and primality
- Parity
- Odd
- Prime
- Yes
- Squarefree
- Yes
- Möbius μ(n)
- -1
- Mersenne prime
- 2^3 − 1
- Twin prime
- Yes — paired with 5
- Nearest primes
- 5 ← → 11
Leaves remainder 1 on division by 2.
Divisible only by 1 and itself.
1 distinct prime factor, 1 with multiplicity.
No prime divides it twice.
(−1) to the power of 1 distinct prime factors.
A gap of 6 between them.
Divisors
- Aliquot sum
- 1
- Classification
- Deficient
1, 7
The proper divisors — everything except n itself.
Its proper divisors fall short by 6.
How many integers from 1 to n share no factor with n.
Sums and additive structure
- Sum of two squares
- No
- Sum of three squares
- No
- Sum of four squares
- Yes
A prime congruent to 3 mod 4 divides it an odd number of times, which rules it out.
Excluded by Legendre: it has the form 4^a(8b + 7).
Lagrange's four-square theorem: every non-negative integer is, without exception.
Shapes and sequences
- Lucas number
- Yes — index 4
Digit curiosities
- Happy number
- Yes
- Armstrong number
- Yes, trivially
- Harshad number
- Yes
- Collatz trajectory
- 16 steps to 1
Repeatedly summing the squares of its digits reaches 1.
Every single-digit number equals itself raised to the first power, so all ten qualify trivially.
Divisible by its digit sum 7 — 7 ÷ 7 = 1.
Peaks at 52 along the way.
Written other ways
- Binary
- 111
- Octal
- 7
- Base 36
- 7
- Roman numerals
- VII
- In words
- seven
- Scientific notation
- 7 × 10^0
Is 7 a prime number?
Yes. 7 has no divisors other than 1 and itself.
Nearby numbers
Other numeral systems
Beyond the bases and Roman numerals above, these notations write 7 their own way.
- Greek (alphabetic)
- Ζʹ
- Tamil
- ௭
References
Further reading: Wikipedia · MathWorld · Wikidata
Notations, naming and the links above come from Wikidata, whose structured data is dedicated to the public domain under CC0-1.0. Retrieved 2026-10-07.