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A two-digit number less than 80 and greater than 65 is divisible by 2 and 9. Name the number.(1 point)
Remaining Attempts : 3

1 answer

The two-digit numbers that are less than 80 and greater than 65 are 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, and 79.

Among these, we need to find a number that is divisible by both 2 and 9.

A number is divisible by 2 if it is even, and it is divisible by 9 if the sum of its digits is a multiple of 9.

Checking the even numbers in the range (66, 68, 70, 72, 74, 76, 78):

  1. 66: Sum of digits = 6 + 6 = 12 (not divisible by 9)
  2. 68: Sum of digits = 6 + 8 = 14 (not divisible by 9)
  3. 70: Sum of digits = 7 + 0 = 7 (not divisible by 9)
  4. 72: Sum of digits = 7 + 2 = 9 (divisible by 9)
  5. 74: Sum of digits = 7 + 4 = 11 (not divisible by 9)
  6. 76: Sum of digits = 7 + 6 = 13 (not divisible by 9)
  7. 78: Sum of digits = 7 + 8 = 15 (not divisible by 9)

The only number that meets the criteria is 72.

Therefore, the number is 72.