What single digit number whose perfect square has 7 factors?

Answer 1

Single Digit numbers: 1,2,3,4,5,6,7,8,9

Perfect squares of single digit numbers

1: 1

2: 4

3: 9

4: 16

5: 25

6: 36

7: 49

8: 64

9: 81

Factor pairs of Perfect squares

1: 1,1

4: 1,4; 2,2

9: 1,9; 3,3

16: 1,16; 2,8; 4,4

25: 1,25; 5,5

36: 1,36; 2,18; 3,12; 4,9; 6,6

49: 1,49; 7,7

64: 1,64; 2,32; 4,16, 8,8

81: 1,81; 3,27, 9,9

Factors of Perfect squares

1: 1

4: 1,2,4

9: 1,3,9

16: 1,2,4,8,16

25: 1,5,25

36: 1,2,3,4,6,9,12,18,36

49: 1,7,49

64: 1,2,4,8,16,32,64

81: 1,3,9,27,81

# of Factors of Perfect squares

1: 1

4: 3

9: 3

16: 5

25: 3

36: 9

49: 3

64: 7

81: 5

# of Factors of Perfect squares of single digit numbers

1: 1

2: 3

3: 3

4: 5

5: 3

6: 9

7: 3

8: 7

9: 5

So the answer is the number 8