Divide 6885 by 45 in your head

Question

Solve in your head, no long division. What is 6885 \div 45? Aim: under 15 seconds.

Accepted Answer

Factor the divisor: 45 = 9 	imes 5. Check both: - Divisible by 5? It ends in 5, yes. - Divisible by 9? Digit sum 6+8+8+5 = 27, divisible by 9, yes. So the answer is whole. Divide by the two factors in turn, easiest first: 6885 \div 5 = 1377, \qquad 1377 \div 9 = 153. (The second step uses the same digit-sum shortcut: 1377 has digit sum 18, and 9 	imes 153 = 1377.) Therefore 6885 \div 45 = 153. Quick check: 45 	imes 153 = 45 	imes 150 + 45 	imes 3 = 6750 + 135 = 6885. Correct. Takeaway. Composite divisors dissolve into a chain of easy divisions: \div 45 = \div 5 then \div 9. Factor the di…

Divide 6885 by 45 in your head

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