
Shortcut Trick
In successive division, the given quotients are treated as remainders to find the original number.
Work backward from the last divisor: [(Last Divisor × Last Quotient) + Last Remainder].
Assume the minimal final quotient is 1: (6 × 1 + 4) = 10.
Apply to next divisor: (5 × 10 + 3) = 53.
Apply to first divisor: (4 × 53 + 2) = 214.
∴ The correct answer is 214.

Alternate Method
Given:
Divisors = 4, 5, 6
Successive Remainders (given as quotients) = 2, 3, 4
Method: Successive division follows the rule: Dividend = (Divisor × Quotient) + Remainder. In successive division, the quotient of one step becomes the dividend for the next.
N ÷ 4 rem 2 53 ÷ 5 rem 3 10 ÷ 6 rem 4 1 Calculation: [(6 × 1 + 4) × 5 + 3] × 4 + 2 = 214
Calculation:
Assume the final quotient after dividing by 6 is 1.
⇒ Number before last division (Quotient 2) = (6 × 1) + 4 = 10
⇒ Number before second division (Quotient 1) = (5 × 10) + 3 = 53
⇒ Original Number (N) = (4 × 53) + 2 = 214
∴ The correct answer is 214.

Additional Information
Successive Division Formula
For divisors d1, d2, d3 and remainders r1, r2, r3, the number N = d1d2r3 + d1r2 + r1 (assuming final quotient is 0).
General Solution
All such numbers can be represented as (LCM of divisors × k) + Smallest Number. For this case, N = 120k + 214.
Successive vs. Simultaneous Division
In successive division, the quotient of the first division becomes the dividend for the second. In simultaneous division, the original number is divided by each divisor independently.