Long Division Calculator
Step-by-step long division with remainder. Shows every digit step clearly. Extended: decimal division with repeating detection and polynomial division. Professional: modular arithmetic and Chinese Remainder Theorem.
Quick Calculator Get a fast estimate
4587 ÷ 7
655 remainder 2
Quotient
655
Remainder
2
Decimal result
655.28571429
Verification
7×655+2=4587
Step-by-step working (4 steps)
- Bring down 4: 4 ÷ 7 = 0 remainder 4 (0×7=0, 4−0=4)
- Bring down 5: 45 ÷ 7 = 6 remainder 3 (6×7=42, 45−42=3)
- Bring down 8: 38 ÷ 7 = 5 remainder 3 (5×7=35, 38−35=3)
- Bring down 7: 37 ÷ 7 = 5 remainder 2 (5×7=35, 37−35=2)
How to Use the Long Division Calculator
Enter the dividend (number being divided) and the divisor. The calculator shows each step of the long division process, including the partial dividend, quotient digit, multiplication, and subtraction at each stage.
The Extended Calculator adds decimal division with repeating pattern detection and polynomial division. The Professional Calculator covers modular arithmetic and the Chinese Remainder Theorem.
Need more detail?
Extended Calculator More options, charts, and scenario comparison
4587 ÷ 7
655 R 2
Long Division Algorithm
4587 ÷ 7:
Step 1: 4 ÷ 7 = 0, bring down 5 → 45 ÷ 7 = 6 R 3
Step 2: Bring down 8 → 38 ÷ 7 = 5 R 3
Step 3: Bring down 7 → 37 ÷ 7 = 5 R 2
Result: 655 remainder 2
Verify: 7×655 + 2 = 4585 + 2 = 4587 ✓
Division algorithm: a = q×b + r, where 0 ≤ r < b
Decimal Division and Repeating Decimals
| Fraction | Decimal | Type |
|---|---|---|
| 1/4 | 0.25 | Terminating |
| 1/3 | 0.333... | Repeating |
| 1/6 | 0.1666... | Mixed repeating |
| 1/7 | 0.142857142857... | Repeating (period 6) |
| 1/8 | 0.125 | Terminating |
Need full precision?
Professional Calculator Complete parameters, sensitivity analysis, and detailed breakdown
Compute a ★ b (mod m)
(17+8) mod 5 = 25 mod 5
≡ 0 (mod 5)
a mod m
2
b mod m
3
Frequently Asked Questions
Bring digits down one at a time. Divide the current partial dividend by the divisor, write the quotient digit, subtract divisor×quotient, then bring down the next digit. Repeat until all digits are processed.
The remainder r satisfies: dividend = quotient × divisor + r, where 0 ≤ r < divisor. Example: 22÷6=3 remainder 4, because 6×3+4=22.
Decimals from fractions with denominators that have prime factors other than 2 and 5 always repeat. 1/3=0.3̄, 1/7=0.142857̄. The period (length of repeating block) divides φ(denominator).
a mod m gives the remainder when a is divided by m. 25 mod 7 = 4. Used in clock arithmetic (hours are mod 12 or 24), cryptography (RSA uses large modular exponentiation), and hash functions.
If moduli m₁,m₂,...,mₙ are pairwise coprime, then the system x≡r₁(mod m₁),...,x≡rₙ(mod mₙ) has a unique solution modulo M=m₁×m₂×...×mₙ. The CRT is fundamental in cryptography and number theory.