Number dictionary · Exact arithmetic
120: factors and number facts
one hundred twenty is an even number and is composite. Its 16 positive divisors form 8 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- one hundred twenty
- Roman numeral
- CXX
- Prime factorization
- 2^3 × 3 × 5
- Digital root
- 3
All factors of 120
A positive factor divides 120 with no remainder. In ascending order, the complete list is:
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
Factor pairs
- 1 × 120 = 120
- 2 × 60 = 120
- 3 × 40 = 120
- 4 × 30 = 120
- 5 × 24 = 120
- 6 × 20 = 120
- 8 × 15 = 120
- 10 × 12 = 120
Each pair describes an arrangement of 120 items into equal rows. The pairs have different row and column counts; 120 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 16
- Sum of all divisors
- 360
- Sum excluding 120
- 240
- Classification
- abundant
120 is abundant because its proper divisors add to 240, which is greater than 120.
Prime factorization of 120
120 = 2^3 × 3 × 5
Repeated division, step by step
- 120 ÷ 2 = 60
- 60 ÷ 2 = 30
- 30 ÷ 2 = 15
- 15 ÷ 3 = 5
- 5 ÷ 5 = 1
Multiply the prime divisors in these steps to reconstruct 120. An exponent records how many times the same prime occurs. The divisor-count calculation is (3 + 1) × (1 + 1) × (1 + 1) = 16.
The preceding prime is 113. The next larger prime is 127. The factor list above explains why 120 is composite.
Learn the factorization method120 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | one hundred twenty |
| Roman numeral | CXX |
| Binary (base 2) | 1111000 |
| Octal (base 8) | 170 |
| Decimal (base 10) | 120 |
| Hexadecimal (base 16) | 78 |
Check the binary conversion
Read 1111000 from right to left using place values 1, 2, 4, 8 and successive powers of two. Keep the values whose bit is 1:
64 + 32 + 16 + 8 = 120
Check the hexadecimal conversion
7 × 16^1 + 8 × 16^0 = 120
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 120
- 120 squared
- 120 × 120 = 14,400
- 120 cubed
- 120 × 120 × 120 = 1,728,000
- Square root
- ≈ 10.954451
- Simplified radical
- 2√30
120 lies between 100 (10²) and 121 (11²), so it is not a perfect square. It is not a perfect cube.
120 is triangular: it is the sum of the integers from 1 through 15.
Distinguish a square from a square rootMultiplication table for 120
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 | 60 | 0 | Yes |
| 3 | 40 | 0 | Yes |
| 4 | 30 | 0 | Yes |
| 5 | 24 | 0 | Yes |
| 6 | 20 | 0 | Yes |
| 7 | 17 | 1 | No |
| 8 | 15 | 0 | Yes |
| 9 | 13 | 3 | No |
| 10 | 12 | 0 | Yes |
| 11 | 10 | 10 | No |
| 12 | 10 | 0 | Yes |
For example, 120 = 7 × 17 + 1. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 120
120 contains 3 decimal digits. Its digit sum is 1 + 2 + 0 = 3.
- 120: 1 + 2 + 0 = 3
The digital root is 3. Reversing its digits gives 021; 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, 120/100 simplifies to 6/5 by dividing both terms by their greatest common divisor, 20. Its decimal value is 1.2. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 120 and 12 is 12. Their least common multiple is 120. The identity GCD × LCM = 120 × 12 = 1440 checks both results.
Work through GCF and LCMQuestions about 120
What are the factors of 120?
The positive factors are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120. There are 16 factors, including 1 and 120.
Is 120 a prime number?
No. 120 is composite: 2^3 × 3 × 5 = 120.
How do you write 120 in Roman numerals?
120 is CXX in standard subtractive Roman numeral notation.
What is the binary representation of 120?
120 in decimal is 1111000 in base 2. Adding its active place values gives 64 + 32 + 16 + 8 = 120.
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 120
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 120 add to 3. 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.