Divide 3752 by 8 in your head

Question

Solve in your head, no long division. What is 3752 \div 8? Aim: under 15 seconds.

Accepted Answer

First confirm it divides evenly: a number is divisible by 8 when its last three digits are. Here 752 = 8 	imes 94, so 3752 is divisible by 8 and the answer is whole. Since 8 = 2^3, dividing by 8 is halving three times: 3752 \xrightarrow{\div 2} 1876 \xrightarrow{\div 2} 938 \xrightarrow{\div 2} 469. So 3752 \div 8 = 469. Quick check: 8 	imes 469 = 8 	imes 470 - 8 = 3760 - 8 = 3752. Correct. Takeaway. Break a divisor into small factors and divide by them in turn: \div 8 is three halvings, \div 4 is two. Repeated halving is far easier to hold in your head than long division, and the last-thr…

Divide 3752 by 8 in your head

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