Number dictionary · Exact arithmetic
84: factors and number facts
eighty-four is an even number and is composite. Its 12 positive divisors form 6 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- eighty-four
- Roman numeral
- LXXXIV
- Prime factorization
- 2^2 × 3 × 7
- Digital root
- 3
All factors of 84
A positive factor divides 84 with no remainder. In ascending order, the complete list is:
1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Factor pairs
- 1 × 84 = 84
- 2 × 42 = 84
- 3 × 28 = 84
- 4 × 21 = 84
- 6 × 14 = 84
- 7 × 12 = 84
Each pair describes an arrangement of 84 items into equal rows. The pairs have different row and column counts; 84 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 12
- Sum of all divisors
- 224
- Sum excluding 84
- 140
- Classification
- abundant
84 is abundant because its proper divisors add to 140, which is greater than 84.
Prime factorization of 84
84 = 2^2 × 3 × 7
Repeated division, step by step
- 84 ÷ 2 = 42
- 42 ÷ 2 = 21
- 21 ÷ 3 = 7
- 7 ÷ 7 = 1
Multiply the prime divisors in these steps to reconstruct 84. An exponent records how many times the same prime occurs. The divisor-count calculation is (2 + 1) × (1 + 1) × (1 + 1) = 12.
The preceding prime is 83. The next larger prime is 89. The factor list above explains why 84 is composite.
Learn the factorization method84 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | eighty-four |
| Roman numeral | LXXXIV |
| Binary (base 2) | 1010100 |
| Octal (base 8) | 124 |
| Decimal (base 10) | 84 |
| Hexadecimal (base 16) | 54 |
Check the binary conversion
Read 1010100 from right to left using place values 1, 2, 4, 8 and successive powers of two. Keep the values whose bit is 1:
64 + 16 + 4 = 84
Check the hexadecimal conversion
5 × 16^1 + 4 × 16^0 = 84
Hexadecimal uses A through F for digit values 10 through 15. These notations represent the same quantity; changing the base does not change the integer.
Square, cube and square root of 84
- 84 squared
- 84 × 84 = 7,056
- 84 cubed
- 84 × 84 × 84 = 592,704
- Square root
- ≈ 9.165151
- Simplified radical
- 2√21
84 lies between 81 (9²) and 100 (10²), so it is not a perfect square. It is not a perfect cube.
84 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 84.
Distinguish a square from a square rootMultiplication table for 84
These are the first twelve positive multiples. Unlike the finite factor list, the sequence of multiples continues without an upper limit.
Divisibility checks
| Divide by | Whole quotient | Remainder | Divides exactly? |
|---|---|---|---|
| 2 | 42 | 0 | Yes |
| 3 | 28 | 0 | Yes |
| 4 | 21 | 0 | Yes |
| 5 | 16 | 4 | No |
| 6 | 14 | 0 | Yes |
| 7 | 12 | 0 | Yes |
| 8 | 10 | 4 | No |
| 9 | 9 | 3 | No |
| 10 | 8 | 4 | No |
| 11 | 7 | 7 | No |
| 12 | 7 | 0 | Yes |
For example, 84 = 7 × 12 + 0. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 84
84 contains 2 decimal digits. Its digit sum is 8 + 4 = 12.
- 84: 8 + 4 = 12
- 12: 1 + 2 = 3
The digital root is 3. Reversing its digits gives 48; it is not a decimal palindrome. Digit patterns depend on the notation being used.
Digital-root arithmetic always finishes at a single digit for a positive integer. Some numerology methods stop at 11, 22 or 33 instead; that is a separate interpretive convention.
Fractions and a worked comparison
As a fraction of 100, 84/100 simplifies to 21/25 by dividing both terms by their greatest common divisor, 4. Its decimal value is 0.84.
The greatest common divisor of 84 and 12 is 12. Their least common multiple is 84. The identity GCD × LCM = 84 × 12 = 1008 checks both results.
Work through GCF and LCMQuestions about 84
What are the factors of 84?
The positive factors are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84. There are 12 factors, including 1 and 84.
Is 84 a prime number?
No. 84 is composite: 2^2 × 3 × 7 = 84.
How do you write 84 in Roman numerals?
84 is LXXXIV in standard subtractive Roman numeral notation.
What is the binary representation of 84?
84 in decimal is 1010100 in base 2. Adding its active place values gives 64 + 16 + 4 = 84.
Methods and reference definitions
Number JD calculates each result from the integer on this page. Positive factors are enumerated in pairs; repeated division gives the prime factorization; place values verify base conversions. Decimal square roots are rounded to six places when irrational.
NUMBER JOURNAL / JD
A reflective note on 84
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 84 add to 12. That arithmetic result is separate from the cultural symbolism of the pattern. If this number matters to you, write down what you noticed and choose one grounded action rather than treating the sighting as a prediction.