Q6

Realise that 49 = 7 x 7
If 49 is a factor (number divisible by 49), then it is also divisible by 7. So 7 is one of the factors.

So we have 1,2,7,49.

If number is divisible by 2 and 7, the number is also divisible by (2 x 7)
2 x 7 = 14

14 is another factor.
(By the way, this only holds if both factors are prime factors)

(Bonus: the number is 98.

98 can be divided by 1,2,7,14,49,98. That's 6 factors)

Q7

you have 4, 6 and 7.

You can form 46,47,64,67,74,76.

We try with largest 2 digit number first, 76.

76 ÷ 4 = 19

So it's 76

8a)

We have 6,5,2,8.

For any multiple of 5, the last digit must be 0 or 5. Since we have no 0s and one 5 here, we put 5 as the last digit.

_ _ _ 5

So we need to fill in the first 3 digits.


We want the smallest multiple of 5.

So we should try with smallest thousands digits first , which is 2.

2 _ _ 5


We have 6 and 8 left.
The hundreds digit should be as small as possible. We use 6

Our number is 2685

8b)


For number closest to 6000, it should be
5 _ _ _ or 6 _ _ _


For 5 _ _ _ , it should be as large as possible so we can be as close as possible to 6000.

Largest number = 5862
(Idea here is that the hundreds place should be larger than tens place, which is larger than ones place)



For 6 _ _ _ , it should be as small as possible so we can be as close as possible to 6000.

Smallest number = 6258
(Idea here is that the hundreds place should be smaller than tens place, which is smaller than ones place).


We compare 5862 and 6258.

6000 - 5862 = 138
6258 - 6000 = 258

So 5862 is closer to 6000 than 6258 is.

The answer is 5862