Number dictionary · Exact arithmetic
752: factors and number facts
seven hundred fifty-two is an even number and is composite. Its 10 positive divisors form 5 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- seven hundred fifty-two
- Roman numeral
- DCCLII
- Prime factorization
- 2^4 × 47
- Digital root
- 5
All factors of 752
A positive factor divides 752 with no remainder. In ascending order, the complete list is:
1, 2, 4, 8, 16, 47, 94, 188, 376, 752
Factor pairs
- 1 × 752 = 752
- 2 × 376 = 752
- 4 × 188 = 752
- 8 × 94 = 752
- 16 × 47 = 752
Each pair describes an arrangement of 752 items into equal rows. The pairs have different row and column counts; 752 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 10
- Sum of all divisors
- 1488
- Sum excluding 752
- 736
- Classification
- deficient
752 is deficient because its proper divisors add to 736, which is less than 752.
Prime factorization of 752
752 = 2^4 × 47
Repeated division, step by step
- 752 ÷ 2 = 376
- 376 ÷ 2 = 188
- 188 ÷ 2 = 94
- 94 ÷ 2 = 47
- 47 ÷ 47 = 1
Multiply the prime divisors in these steps to reconstruct 752. An exponent records how many times the same prime occurs. The divisor-count calculation is (4 + 1) × (1 + 1) = 10.
The preceding prime is 751. The next larger prime is 757. The factor list above explains why 752 is composite.
Learn the factorization method752 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | seven hundred fifty-two |
| Roman numeral | DCCLII |
| Binary (base 2) | 1011110000 |
| Octal (base 8) | 1360 |
| Decimal (base 10) | 752 |
| Hexadecimal (base 16) | 2F0 |
Check the binary conversion
Read 1011110000 from right to left using place values 1, 2, 4, 8 and successive powers of two. Keep the values whose bit is 1:
512 + 128 + 64 + 32 + 16 = 752
Check the hexadecimal conversion
2 × 16^2 + 15 × 16^1 + 0 × 16^0 = 752
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 752
- 752 squared
- 752 × 752 = 565,504
- 752 cubed
- 752 × 752 × 752 = 425,259,008
- Square root
- ≈ 27.422618
- Simplified radical
- 4√47
752 lies between 729 (27²) and 784 (28²), so it is not a perfect square. It is not a perfect cube.
752 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 752.
Distinguish a square from a square rootMultiplication table for 752
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 | 376 | 0 | Yes |
| 3 | 250 | 2 | No |
| 4 | 188 | 0 | Yes |
| 5 | 150 | 2 | No |
| 6 | 125 | 2 | No |
| 7 | 107 | 3 | No |
| 8 | 94 | 0 | Yes |
| 9 | 83 | 5 | No |
| 10 | 75 | 2 | No |
| 11 | 68 | 4 | No |
| 12 | 62 | 8 | No |
For example, 752 = 7 × 107 + 3. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 752
752 contains 3 decimal digits. Its digit sum is 7 + 5 + 2 = 14.
- 752: 7 + 5 + 2 = 14
- 14: 1 + 4 = 5
The digital root is 5. Reversing its digits gives 257; 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, 752/100 simplifies to 188/25 by dividing both terms by their greatest common divisor, 4. Its decimal value is 7.52. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 752 and 12 is 4. Their least common multiple is 2256. The identity GCD × LCM = 752 × 12 = 9024 checks both results.
Work through GCF and LCMQuestions about 752
What are the factors of 752?
The positive factors are 1, 2, 4, 8, 16, 47, 94, 188, 376, 752. There are 10 factors, including 1 and 752.
Is 752 a prime number?
No. 752 is composite: 2^4 × 47 = 752.
How do you write 752 in Roman numerals?
752 is DCCLII in standard subtractive Roman numeral notation.
What is the binary representation of 752?
752 in decimal is 1011110000 in base 2. Adding its active place values gives 512 + 128 + 64 + 32 + 16 = 752.
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 752
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 752 add to 14. 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.