How many six digit numbers are in the form 225A7B such that the number is divisible by 36
Answers
Answer:
A = '5' and B = '7'
Step-by-step explanation:
225576÷36=6266
There are 180 six-digit numbers in the form 225A7B that are divisible by 36.
For a number to be divisible by 36, it must be divisible by both 4 and 9.
A number is divisible by 4 if its last two digits are divisible by 4. Therefore, the number 225A7B is divisible by 4 if the two-digit number A7 is divisible by 4. The only possible values for A that make A7 divisible by 4 are 04, 08, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, and 80. So there are 20 choices for A.
A number is divisible by 9 if the sum of its digits is divisible by 9. The sum of the digits in the number 225A7B is 2 + 2 + 5 + A + 7 + B = 16 + A + B. For the sum to be divisible by 9, A + B must be a multiple of 9. There are 9 possible values of A and B that make A + B a multiple of 9: (0,9), (1,8), (2,7), (3,6), (4,5), (5,4), (6,3), (7,2), and (8,1). Therefore, there are 9 choices for the pair (A,B).
To count the total number of six-digit numbers in the form 225A7B that are divisible by 36, we need to multiply the number of choices for A and B:
Number of choices = 20 x 9 = 180
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