84
LXXXIV
1010100
The number 84 — factors and divisors
Abundant
84 = 2² × 3 × 7. It has 12 divisors, adding up to 224.
Its divisors, itself excluded, add up to more than the number.
Laid out as dots
It fits as 7 × 12. The more divisors, the closer to a square.
- Prime factors
- 2² × 3 × 7
- Divisors
- 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
- Sum of divisors
- 224
- Sum without itself
- 140
- Coprime below it
- 24
- Digit sum
- 12
- Digital root
- 3
- Roman numeral
- LXXXIV
- Binary
- 1010100
- Octal
- 124
- Hexadecimal
- 54
- Base 36
- 2C
- Bits
- 7 bits
- Collatz steps
- 9 steps · peaks at 84
- Prime before
- 83
- Prime after
- 89
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 84 a prime number?
No. It breaks down into 2² × 3 × 7.
Q. What are the divisors of 84?
1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 — 12 divisors in all, adding up to 224.
Q. How is 84 written in binary?
1010100, which is 7 bits. In hexadecimal it is 54.
Q. How many Collatz steps does 84 take?
It reaches 1 in 9, peaking at 84 on the way.