144
CXLIV
10010000
The number 144 — factors and divisors
Abundant
144 = 2⁴ × 3². It has 15 divisors, adding up to 403.
Its divisors, itself excluded, add up to more than the number.
Families it belongs to
Square
A number times itself — the dots lay out as a square.
Fibonacci
It sits in the run where each number is the sum of the two before it.
Laid out as dots
It fits as 12 × 12. The more divisors, the closer to a square.
- Prime factors
- 2⁴ × 3²
- Divisors
- 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
- Sum of divisors
- 403
- Sum without itself
- 259
- Coprime below it
- 48
- Digit sum
- 9
- Digital root
- 9
- Roman numeral
- CXLIV
- Binary
- 10010000
- Octal
- 220
- Hexadecimal
- 90
- Base 36
- 40
- Bits
- 8 bits
- Collatz steps
- 23 steps · peaks at 144
- Prime before
- 139
- Prime after
- 149
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.
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200
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 144 a prime number?
No. It breaks down into 2⁴ × 3².
Q. What are the divisors of 144?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144 — 15 divisors in all, adding up to 403.
Q. How is 144 written in binary?
10010000, which is 8 bits. In hexadecimal it is 90.
Q. How many Collatz steps does 144 take?
It reaches 1 in 23, peaking at 144 on the way.