Divide 8613 by 11 in your head

Question

Solve in your head, no long division. What is 8613 \div 11? Aim: under 15 seconds.

Accepted Answer

Alternating digit sum (from the right): 3 - 1 + 6 - 8 = 0. A result of 0 (or any multiple of 11) means 8613 is divisible by 11, so the answer is a whole number. Fast route, anchor on an easy multiple of 11: 11 	imes 780 = 8580, \qquad 8613 - 8580 = 33 = 11 	imes 3, so 8613 \div 11 = 780 + 3 = 783. Quick check: 11 	imes 783 = 7830 + 783 = 8613. Correct. Takeaway. Each small divisor has its own clean divisibility test: digit sum for 3 and 9, alternating digit sum for 11, last digits for 2, 4, 5, 8. Confirm divisibility, anchor on a round multiple, and patch the remainder.

Divide 8613 by 11 in your head

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