Note: `(6 + 6 + 7) - (2 + 8 + 9) = 0,` So, 978626 is divisible by 11

Note: `(6 + 6 + 7) - (2 + 8 + 9) = 0,` So, 978626 is divisible by 11

Note: `(1/6)^(12) xx (8)^(25) xx (3/4)^(15)` `= 1/(2^(12) xx 3^(12)) xx (2^3)^(25) xx 3^(15)/(2^15 xx 2^15)` `= (2^75 xx 3^15)/(2^42 xx 3^12)` `= 2^33 xx 3^3` :. Total number of prime factors `= (33 + 3) = 36`

Note: Not available

Note: Let the given number be x. The when divided by 32. suppose gives the quotient k. Then, `x = 32 k + 29 = 8 xx (4 k + 3) + 5` Thus, when x is divided by 8. it gives `(4 k + 3)` as quotient and 5 as remainder.

Note: `a/c = a/b xx b/c = 4/5 xx 15/16 = 3/4` `:. (c^2 - a^2)/(c^2 + a^2)` `= (1 - a^2/c^2)/(1 + a^2/c^2)` `= (1 - 9/16)/(1 + 9/16)` `= 7/16 xx 16/25` `= 7/25`

Note: From among the given numbers, 923872 is the only number, whose last 3 digit form 872, which divisible by 8.`

Note: 18962 when divided by 13 leaves the remainder 8. :. Number to be added = (13 - 8) = 5

Note: Not available

Note: 437950 is the only number among given numbers s.t 437950` = 5 xx 87590` `= 5 xx 5 xx 17518,` which has 25 as a factors