Divisibility

Number Theory Level 2

Without using a calculator

Which of the following is/are divisible by 8

I 74832

II 23868

III 13552

Neither of the above I and III All of the above II and III I only II only III only I and II

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Ooi Ming Yang by Ooi Ming Yang , 30, Malaysia

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1 solution

Ooi Ming Yang
Apr 8, 2016

Divisibility rule for 8

i) the last 3 digits of the number is divisible by 8

74 832 --- 832 8 = 104 \frac {832}{8} = 104 (Yes)

23 868 (obviously can't be divisible by 8) --- 868 8 = 108 R 4 \frac {868}{8} = 108 R 4 (No)

13 552 --- 552 8 = 69 \frac {552}{8} = 69 (Yes)

Therefore, I and III is divisible by 8.

ii) 4 ( H u n d r e d s ) + 2 ( T e n s ) + ( O n e s ) 4(Hundreds)+2(Tens)+(Ones) of the number is divisible by 8

74832 --- 4 ( 8 ) + 2 ( 3 ) + 2 = 40 4(8)+2(3)+2=40

40 8 = 5 \frac {40}{8}=5 (Yes)

23868 --- 4 ( 8 ) + 2 ( 6 ) + 8 = 52 4(8)+2(6)+8=52

52 8 = 6 R 4 \frac {52}{8}=6 R 4 (No)

13552 ---- 4 ( 5 ) + 2 ( 5 ) + 2 = 32 4(5)+2(5)+2=32

32 8 = 4 \frac {32}{8}=4 (Yes)

Therefore, I and III is divisible by 8.

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