Long Division Calculator

Step-by-step:

1. 8 doesn't fit into 1, so look at 12. 8 fits into 12 once (8 × 1 = 8). Write 1 above the 2.
2. Subtract: 12 - 8 = 4.
3. Bring down the 5 to make 45.
4. 8 fits into 45 five times (8 × 5 = 40). Write 5 above the 5.
5. Subtract: 45 - 40 = 5. No more digits to bring down.

Answer: 125 ÷ 8 = 15 remainder 5 (or 15.625 as a decimal)

Check: (15 × 8) + 5 = 120 + 5 = 125 ✓

Answer: 2847 ÷ 23 = 123 remainder 18

Check: (123 × 23) + 18 = 2829 + 18 = 2847 ✓

Answer: 504 ÷ 7 = 72 (exactly, no remainder)

When a number divides evenly, we say it's a factor. 7 is a factor of 504.

When the dividend is smaller than the divisor, the quotient is 0 and the entire dividend becomes the remainder.

Answer: 53 ÷ 100 = 0 remainder 53

As a decimal: 0.53. As a fraction: 53/100.

Long division is a method for dividing large numbers by breaking the problem into a series of smaller, easier steps. It involves repeatedly dividing, multiplying, and subtracting until no digits remain, producing a quotient and possibly a remainder.

Long division follows four repeating steps: (1) Divide—determine how many times the divisor fits into the current portion of the dividend; (2) Multiply—multiply the divisor by that number; (3) Subtract—subtract the product from the current portion; (4) Bring down—bring down the next digit and repeat until no digits remain.

The quotient is the main answer to a division problem—how many whole times the divisor fits into the dividend. The remainder is what's left over after the division is complete, representing the portion of the dividend that cannot be evenly divided.

Multiply the quotient by the divisor, then add the remainder. The result should equal the original dividend. Formula: (Quotient × Divisor) + Remainder = Dividend. For example, 125 ÷ 8 = 15 R 5 can be verified: (15 × 8) + 5 = 120 + 5 = 125.

When the dividend is smaller than the divisor, the quotient is 0 and the remainder equals the dividend. For example, 5 ÷ 8 = 0 remainder 5, because 8 does not fit into 5 at all.

Yes. To continue dividing past the remainder, add a decimal point to the quotient and zeros to the remainder, then continue the division process. For example, 125 ÷ 8 = 15.625 when carried out to three decimal places.

Long division builds foundational understanding of how division works and develops number sense. It's essential for polynomial division in algebra, understanding ratios and proportions, and working with fractions. The systematic approach also strengthens problem-solving skills.

Short division is a condensed form where intermediate calculations are done mentally and only the quotient is written. Long division writes out every step explicitly, making it easier to follow and learn from, especially with larger numbers.

"R" stands for "remainder." When you see 15 R 5, it means the quotient is 15 and the remainder is 5. The remainder is what's left over when the dividend cannot be evenly divided by the divisor.

When the divisor doesn't fit into your current working number, write 0 in the quotient and bring down the next digit. For example, in 1008 ÷ 4: 4 goes into 10 twice (8), remainder 2. Bring down 0 to get 20. 4 goes into 20 five times (20). Bring down 8. 4 goes into 8 twice. Answer: 252.

Yes. Any division can be expressed as a fraction: dividend/divisor. For example, 125 ÷ 8 can be written as 125/8, which equals 15 5/8 as a mixed number. The remainder becomes the numerator of the fractional part.

Look at more digits together. For example, in 2847 ÷ 23, you can't divide 23 into 2, so you look at 28 instead. 23 fits into 28 once. Then continue the process with the remaining digits.