Number dictionary · Exact arithmetic
472: factors and number facts
four hundred seventy-two is an even number and is composite. Its 8 positive divisors form 4 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- four hundred seventy-two
- Roman numeral
- CDLXXII
- Prime factorization
- 2^3 × 59
- Digital root
- 4
All factors of 472
A positive factor divides 472 with no remainder. In ascending order, the complete list is:
1, 2, 4, 8, 59, 118, 236, 472
Factor pairs
- 1 × 472 = 472
- 2 × 236 = 472
- 4 × 118 = 472
- 8 × 59 = 472
Each pair describes an arrangement of 472 items into equal rows. The pairs have different row and column counts; 472 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 8
- Sum of all divisors
- 900
- Sum excluding 472
- 428
- Classification
- deficient
472 is deficient because its proper divisors add to 428, which is less than 472.
Prime factorization of 472
472 = 2^3 × 59
Repeated division, step by step
- 472 ÷ 2 = 236
- 236 ÷ 2 = 118
- 118 ÷ 2 = 59
- 59 ÷ 59 = 1
Multiply the prime divisors in these steps to reconstruct 472. An exponent records how many times the same prime occurs. The divisor-count calculation is (3 + 1) × (1 + 1) = 8.
The preceding prime is 467. The next larger prime is 479. The factor list above explains why 472 is composite.
Learn the factorization method472 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | four hundred seventy-two |
| Roman numeral | CDLXXII |
| Binary (base 2) | 111011000 |
| Octal (base 8) | 730 |
| Decimal (base 10) | 472 |
| Hexadecimal (base 16) | 1D8 |
Check the binary conversion
Read 111011000 from right to left using place values 1, 2, 4, 8 and successive powers of two. Keep the values whose bit is 1:
256 + 128 + 64 + 16 + 8 = 472
Check the hexadecimal conversion
1 × 16^2 + 13 × 16^1 + 8 × 16^0 = 472
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 472
- 472 squared
- 472 × 472 = 222,784
- 472 cubed
- 472 × 472 × 472 = 105,154,048
- Square root
- ≈ 21.725561
- Simplified radical
- 2√118
472 lies between 441 (21²) and 484 (22²), so it is not a perfect square. It is not a perfect cube.
472 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 472.
Distinguish a square from a square rootMultiplication table for 472
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 | 236 | 0 | Yes |
| 3 | 157 | 1 | No |
| 4 | 118 | 0 | Yes |
| 5 | 94 | 2 | No |
| 6 | 78 | 4 | No |
| 7 | 67 | 3 | No |
| 8 | 59 | 0 | Yes |
| 9 | 52 | 4 | No |
| 10 | 47 | 2 | No |
| 11 | 42 | 10 | No |
| 12 | 39 | 4 | No |
For example, 472 = 7 × 67 + 3. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 472
472 contains 3 decimal digits. Its digit sum is 4 + 7 + 2 = 13.
- 472: 4 + 7 + 2 = 13
- 13: 1 + 3 = 4
The digital root is 4. Reversing its digits gives 274; 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, 472/100 simplifies to 118/25 by dividing both terms by their greatest common divisor, 4. Its decimal value is 4.72. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 472 and 12 is 4. Their least common multiple is 1416. The identity GCD × LCM = 472 × 12 = 5664 checks both results.
Work through GCF and LCMQuestions about 472
What are the factors of 472?
The positive factors are 1, 2, 4, 8, 59, 118, 236, 472. There are 8 factors, including 1 and 472.
Is 472 a prime number?
No. 472 is composite: 2^3 × 59 = 472.
How do you write 472 in Roman numerals?
472 is CDLXXII in standard subtractive Roman numeral notation.
What is the binary representation of 472?
472 in decimal is 111011000 in base 2. Adding its active place values gives 256 + 128 + 64 + 16 + 8 = 472.
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 472
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 472 add to 13. 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.