4. EXTRA Qs

Question 1

How would you answer this question?

Answer 1

Question 2

How would you answer this question?

Answer 2

Break into prime factors!

Question 3

How do you answer this?

Answer 3

You can fully calculate it, but it helps if you see that its a formula for (x-y)(x-y)

Question 4

How do you answer this?

Answer 4

Question 5

How do you answer this?

Answer 5

Remember this formula:

Question 6

How does this formula work?

Answer 6

e1 is the exponent of the first prime number

e2 is the exponent of the second prime number… etc

Question 7

How do you answer this?

Answer 7

Question 8

What do you have to know about this?

Answer 8

You have to break 30 into prime factors, and understand that the amount of 30’s you can make, depends on the fewest prime factor, which is 5 in this case

Question 9

How do you answer this?

Answer 9

Question 10

How do you answer this?

Answer 10

Question 11

Can you explain why in this question 4 is doubled and not squared to be 16?

Answer 11

20! has 4 factors of 5

20! × 20! = (20!)^2, which has 8 factors of 5

Squaring DOUBLES every prime, so its 8 and NOT 16

Question 12

How do you answer this?

Answer 12

Carry out long division and spot the pattern

Question 13

How do you answer this?

Answer 13

You have to find the number of 5’s in 200!

Question 14

How do you answer this?

Answer 14

Remember you are using 3, so you have 2n = 120, therefore n = 60

Question 15

How do you answer this?

Answer 15

First rewrite the factorials, then find the number of 2’s in each of the factors - and remember to correct for the number you are actually finding (4, and not 2)

Question 16

How do you answer this?

Answer 16

Question 17

How do you answer this?

Answer 17

You HAVE to see that b^2, means that its a perfect square and thus you can determine what a must be

Question 18

If a number is divisible by 6, what other numbers must it be divisible by?

Answer 18

2 and 3

Question 19

How do you answer this?

Answer 19

Question 20

How do you answer this?

Answer 20

Question 21

How do you answer this? (hint: 55 x 14 = 770)

Answer 21