Question 281841: 13. By which of the following number is 98765432 exactly divisible?
A. 9
B. 7
C. 5
D. 8
E. 11
Hello!
Can you please show me step by step how to solve the answer.
Thank you
Tania
Answer by nabla(475)   (Show Source):
You can put this solution on YOUR website! There are indeed numerous ways to do this.
However, an easy way to do this (although not entirely concise!) is to factor 2's.
IE. We know that 2 will factor out as the number is even.
Secondly, we know another 2 will factor out as we will have 16 as the last two digits.
Thirdly, we know yet another 2 will factor out as we will have 58 as the last two digits.
hence, 2^3 is a factor. 2^3=8. hence 8|98765432.
In other words, 8u=98765432 gives u as an integer hence it is exactly divisible.
--- You could solve this using modular arithmetic and a few other ways, but I think this is the most intuitive.
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