72
LXXII
1001000
The number 72 — factors and divisors
Abundant
72 = 2³ × 3². It has 12 divisors, adding up to 195.
Its divisors, itself excluded, add up to more than the number.
Laid out as dots
It fits as 8 × 9. The more divisors, the closer to a square.
- Prime factors
- 2³ × 3²
- Divisors
- 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
- Sum of divisors
- 195
- Sum without itself
- 123
- Coprime below it
- 24
- Digit sum
- 9
- Digital root
- 9
- Roman numeral
- LXXII
- Binary
- 1001000
- Octal
- 110
- Hexadecimal
- 48
- Base 36
- 20
- Bits
- 7 bits
- Collatz steps
- 22 steps · peaks at 72
- Prime before
- 71
- Prime after
- 73
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 72 a prime number?
No. It breaks down into 2³ × 3².
Q. What are the divisors of 72?
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 — 12 divisors in all, adding up to 195.
Q. How is 72 written in binary?
1001000, which is 7 bits. In hexadecimal it is 48.
Q. How many Collatz steps does 72 take?
It reaches 1 in 22, peaking at 72 on the way.