If a seven-digit number 42971K2 is divisible by 44, then the value of K is: 

Given data:

The seven-digit number 42971K2, is divisible by 44.

Concept used:

For a number to be divisible by 44,

it should be divisible by 4 and 11 both.

Divisibility Rule of 4:
A number is divisible by 4 if the number formed by the last two digits of the given number is divisible by 4.

Divisibility Rule of 11:
A number is divisible by 11 if the difference between the sum of digits at odd places and the sum of digits at even places, counted from right to left, is either 0 or divisible by 11.

Solution:

For divisibility by 4, the last two digits should form a number divisible by 4.

So, possible values for K = 1, 3, 7, and 9.

Using the divisibility rule of 11, 42971K2, the only possible value is 7.

So, K = 7.

Hence, the value of K is 7.