Question

(a) Check if 53064 is divisible by 11 using the divisibility rule. (c)Write the prime factorization of 104 using short division method.

Answer 1

Answer:

For example, let us consider 76945

Sum of digits at odd places : 7 + 9 + 5

Sum of digits at even places : 6 + 4

Difference of two sums = 21 - 10 = 11

Since difference is divisible by 11, the

number 7945 is divisible by 11.

How does this work?

Let us consider 7694, we can write it as

7694 = 7*1000 + 6*100 + 9*10 + 4

The proof is based on below observation:

Remainder of 10i divided by 11 is 1 if i is even

Remainder of 10i divided by 11 is -1 if i is odd

So the powers of 10 only result in values either 1

or -1.

Remainder of "7*1000 + 6*100 + 9*10 + 4"

divided by 11 can be written as :

7*(-1) + 6*1 + 9*(-1) + 4*1

The above expression is basically difference

between sum of even digits and odd digits

Answer 2

Answer:

yes 53064 is divisible by 11 and prime factorization of 104 is 2x2x2x13