21
XXI
10101
The number 21 — factors and divisors
Deficient
21 = 3 × 7. It has 4 divisors, adding up to 32.
Its divisors, itself excluded, add up to less than the number.
Families it belongs to
Triangular
The running total of 1, 2, 3 … — the dots stack into a triangle.
Fibonacci
It sits in the run where each number is the sum of the two before it.
Laid out as dots
It fits as 3 × 7. The more divisors, the closer to a square.
- Prime factors
- 3 × 7
- Divisors
- 1, 3, 7, 21
- Sum of divisors
- 32
- Sum without itself
- 11
- Coprime below it
- 12
- Digit sum
- 3
- Digital root
- 3
- Roman numeral
- XXI
- Binary
- 10101
- Octal
- 25
- Hexadecimal
- 15
- Base 36
- L
- Bits
- 5 bits
- Collatz steps
- 7 steps · peaks at 64
- Prime before
- 19
- Prime after
- 23
The grid
Ten per row, twenty rows. The filled cells are primes — you can see the multiples of 2 and 5 drop out in columns.
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Numbers either side
How to read this
- The prime factors are what the number is made of. The count and sum of divisors both follow from them.
- Add the divisors, take the number away, and you get perfect, abundant or deficient.
- The length of the binary form is the bit count. 255 taking eight digits is what a byte is.
- Collatz: halve it if even, triple it and add one if odd. The count is how many moves reach 1.
Frequently asked questions
Q. Is 21 a prime number?
No. It breaks down into 3 × 7.
Q. What are the divisors of 21?
1, 3, 7, 21 — 4 divisors in all, adding up to 32.
Q. How is 21 written in binary?
10101, which is 5 bits. In hexadecimal it is 15.
Q. How many Collatz steps does 21 take?
It reaches 1 in 7, peaking at 64 on the way.