Which number between 30 and 40 have the greatest number of factors?

Answer 1

(assuming you mean between 30 and 40 inclusive)

Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30 (8 factors)

Factors of 31: 1, 31 (2 factors)

Factors of 32: 1, 2, 4, 8, 16, 32 (6 factors)

Factors of 33: 1, 3, 11, 33 (4 factors)

Factors of 34: 1, 2, 17, 34 (4 factors)

Factors of 35: 1, 5, 7, 35 (4 factors)

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 (9 factors)

Factors of 37: 1, 37 (2 factors)

Factors of 38: 1, 2, 19, 38 (4 factors)

Factors of 39: 1, 3, 13, 39 (4 factors)

Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40 (8 factors)

From this you can see that 36 is the number between 30 and 40 with the greatest number of factors.

Answer 2

To answer this question, we need to break all the numbers down into their prime factors. These are:

30 = 2x3x5

31 = 31

32 = 2x2x2x2x2

33 = 3x11

34 = 2x17

35 = 5x7

36 = 2x2x3x3

37 = 37

38 = 2x19

39 = 3x13

40 = 2x2x2x5

Thus it can be seen that 36 has the greatest possibilities for prime factor combination, and therefore the most factors. These are 1, 2, 3, 4, 6, 9, 12, 18 and 36.

Answer 3

36 has nine factors.