Which of the following is exactly divisible by 13?

[KaB£H1s3]

Is there a quick way to answer this question?

The test paper allows approx 40 seconds per question on average.

Which of the following is exactly divisible by 13?

A 2126
B 387
C 2564
D 1126
E 1183

[Glos18]

So, I had to look this up, but this is how you can work it out quickly. Remove the last digit, multiply that digit by 4 then add the resulting number to the remaining number. Keep going until you have a 2 digit number.

Eg. 2564
4x4 =16 +256 = 272
2x4=8 +27 = 35 (not divisible by 13)

Eg. 1183
3x4 =12 + 118 = 130
0x4 = 0 + 13 = 13 (your answer)

[ToadMum]

So, I had to look this up, but this is how you can work it out quickly. Remove the last digit, multiply that digit by 4 then add the resulting number to the remaining number. Keep going until you have a 2 digit number.

Eg. 2564
4x4 =16 +256 = 272
2x4=8 +27 = 35 (not divisible by 13)

Eg. 1183
3x4 =12 + 118 = 130
0x4 = 0 + 13 = 13 (your answer)

In the case of the latter, one would hope that the candidate would recognise that 130 is divisible and save the time and effort of the last calculation, though .

[KaB£H1s3]

Thanks everyone for the replies

[solimum]

My inclination would be to look for "easy" multiples and look for the differences/remainders:

2126: take off the 26 (2x13) and you're left with 2100, seems unlikely this is a multiple of 13 as we know 2600 would be a multiple, so would 520 so 2100 can't be

387 - this is only 3 away from 390 which would be a multiple so 387 can't be

2564 - that's nearly 2600 but the difference is 36 which is not a multiple

1126 - again take off the 26 and 1100 isn't a multiple of 13

1183 - that's 117 away from 1300, then work out that 117 must be a multiple because it is 13 away from 130

Obviously this requires some understanding of basic multiples of 13 such as 26, 39, 52 (always an important times table to learn a few of I feel, comes into playing cards etc!) and arithmetic but it might be easier for some children with an instinct for how numbers work and is adaptable to similar problems with (say) multiples of 17, whereas learning "rules" for each number (beyond the simple rules for multiples of 2, 5, 10, 3 and 9) can be confusing