Number dictionary · Exact arithmetic
701: factors and number facts
seven hundred one is an odd number and is prime. Its 2 positive divisors form 1 factor pair.
Number JD Editorial Team · Updated 2026-10-08
- In words
- seven hundred one
- Roman numeral
- DCCI
- Prime factorization
- 701
- Digital root
- 8
All factors of 701
A positive factor divides 701 with no remainder. In ascending order, the complete list is:
1, 701
Factor pairs
- 1 × 701 = 701
Each pair describes an arrangement of 701 items into equal rows. The pairs have different row and column counts; 701 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 2
- Sum of all divisors
- 702
- Sum excluding 701
- 1
- Classification
- deficient
701 is deficient because its proper divisors add to 1, which is less than 701.
Prime factorization of 701
701 = 701
Repeated division, step by step
- 701 ÷ 701 = 1
Multiply the prime divisors in these steps to reconstruct 701. Each prime in this factorization occurs once. The divisor-count calculation is (1 + 1) = 2.
The preceding prime is 691. The next larger prime is 709. To check 701 for primality, it is sufficient to test possible divisors from 2 through 26.
Learn the factorization method701 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | seven hundred one |
| Roman numeral | DCCI |
| Binary (base 2) | 1010111101 |
| Octal (base 8) | 1275 |
| Decimal (base 10) | 701 |
| Hexadecimal (base 16) | 2BD |
Check the binary conversion
Read 1010111101 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 + 32 + 16 + 8 + 4 + 1 = 701
Check the hexadecimal conversion
2 × 16^2 + 11 × 16^1 + 13 × 16^0 = 701
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 701
- 701 squared
- 701 × 701 = 491,401
- 701 cubed
- 701 × 701 × 701 = 344,472,101
- Square root
- ≈ 26.476405
- Simplified radical
- √701
701 lies between 676 (26²) and 729 (27²), so it is not a perfect square. It is not a perfect cube.
701 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 701.
Distinguish a square from a square rootMultiplication table for 701
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 | 350 | 1 | No |
| 3 | 233 | 2 | No |
| 4 | 175 | 1 | No |
| 5 | 140 | 1 | No |
| 6 | 116 | 5 | No |
| 7 | 100 | 1 | No |
| 8 | 87 | 5 | No |
| 9 | 77 | 8 | No |
| 10 | 70 | 1 | No |
| 11 | 63 | 8 | No |
| 12 | 58 | 5 | No |
For example, 701 = 7 × 100 + 1. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 701
701 contains 3 decimal digits. Its digit sum is 7 + 0 + 1 = 8.
- 701: 7 + 0 + 1 = 8
The digital root is 8. Reversing its digits gives 107; 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, 701/100 simplifies to 701/100 by dividing both terms by their greatest common divisor, 1. Its decimal value is 7.01. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 701 and 12 is 1. Their least common multiple is 8412. The identity GCD × LCM = 701 × 12 = 8412 checks both results.
Work through GCF and LCMQuestions about 701
What are the factors of 701?
The positive factors are 1, 701. There are 2 factors, including 1 and 701.
Is 701 a prime number?
Yes. The only positive divisors of 701 are 1 and 701.
How do you write 701 in Roman numerals?
701 is DCCI in standard subtractive Roman numeral notation.
What is the binary representation of 701?
701 in decimal is 1010111101 in base 2. Adding its active place values gives 512 + 128 + 32 + 16 + 8 + 4 + 1 = 701.
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 701
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 701 add to 8. 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.