What is the value of M and N respectively? If M39048458N is divisible by 8 &…

Step 1 — Use divisibility by 8:

• The last three digits of the number are 58N, so the number 580–589 must contain a multiple of 8.

• Among 580–589, only 584 is divisible by 8 (8 × 73 = 584). Therefore N = 4.

Step 2 — Use divisibility by 11:

• Write the digits in positions 1 to 10: M, 3, 9, 0, 4, 8, 4, 5, 8, 4 (we substitute N = 4).

• Sum of digits in odd positions = M + 9 + 4 + 4 + 8 = M + 25.

• Sum of digits in even positions = 3 + 0 + 8 + 5 + 4 = 20.

• Difference = (M + 25) − 20 = M + 5. For the number to be divisible by 11, this difference must be 0 or a multiple of 11.

• Since M is a single digit, the only possibility is M + 5 = 11, so M = 6.

Answer: M = 6, N = 4