Answer to Question #199474 in Algebra for Phumzile Zondi

Question

Test the following numbers for divisibility by 6,9 and 11.( Do not divide or fractorise)

a) 6 184 046

b) 21 589 434

Answer 1

Divisibility Rule of 6 : A number is divisible by 6 if its last digit is an even number or zero and the sum of the digits is a multiple of 3.

Divisibility Rule of 9 : If the sum of digits of the number is divisible by 9, then the number itself is divisible by 9.

Divisibility Rule of 11: The difference between the sum of digits at even places and the sum of the digits at odd places is either 0 or divisible by 11.

Now for the above given numbers:

A. 6184046:

Sum of the digit $=29$

Divisibility By 6: It's last digit is an even number but even then it is not divided by 6 as the sum of the digit is not a multiple of 3.

Divisibility By 9: It is not divided by 9 as the sum of digit is not divisible by 9.

Divisibility By 11:Here the difference between the sum of the digits at even places(4,4,1) and the digits at odd places (6,0,8,6) is divisible by 11. Hence the number is divisible by 11.

B. 21589434:

Sum of the digit $= 36$

Divisibility By 6: It's last digit is an even number ,and also the sum of the digit (36) is divisible by 3 so the whole number is divided by 6.

Divisibility By 9: It is divided by 9 as the sum of digit is divisible by 9.

Divisibility By 11:Here the difference between the sum of the digits at even places(2,5,9,3) and the digits at odd places (1,8,4,4) is not divisible by 11. Hence the number is not divisible by 11.