Question

Using divisibility tests, determine which of the following numbers are divisible by 4 and 8:
A. 572
B. 726352
C. 5500
D. 6000
E. 12159
F. 14560
G. 21084
H. 31795072
I. 1700
J. 2150

Answer 1

Hint: We will check the last two digits of all the numbers to check if they are divisible by 4 or not and then do the same using the last 3 digits of all the numbers to check the divisibility by 8.

Complete step-by-step solution:
We will go through each of the option one by one:-
A. 572
We here have the number 572 with us.
Its last 2 digits are 72.
We know that:-
$\Rightarrow 72=4\times 18$
$\therefore$ the number 572 is divisible by 4.
Its last 3 digits are the number itself that is 572.
We know that:-
$\Rightarrow 572=2\times 2\times 11\times 13$
It does not have 8 as its factor.
$\therefore$ the number 572 is not divisible by 8.
B. 726352
We here have the number 726352 with us.
Its last 2 digits are 52.
We know that:-
$\Rightarrow 52=4\times 13$
$\therefore$ the number 726352 is divisible by 4.
Its last 3 digits are 352.
We know that:-
$\Rightarrow 352=8\times 44$
$\therefore$ the number 726352 is divisible by 8.
C. 5500
We here have the number 5500 with us.
Its last 2 digits are 00.
0 is definitely divisible by 4.
$\therefore$ the number 5500 is divisible by 4.
Its last 3 digits are 500.
We know that:-
$\Rightarrow 500=2\times 2\times 5\times 5\times 5$
It does not have 8 as its factor.
$\therefore$ the number 5500 is not divisible by 8.
D. 6000
We here have the number 6000 with us.
Its last 2 digits are 00.
0 is definitely divisible by 4.
$\therefore$ the number 6000 is divisible by 4.
Its last 3 digits are 000.
0 is definitely divisible by 8.
$\therefore$ the number 6000 is divisible by 8.
E. 12159
We here have the number 12159 with us.
Its last 2 digits are 59.
Since 59 is a prime number.
$\therefore$ the number 12159 is not divisible by 4.
Its last 3 digits are 159.
We know that:-
$\Rightarrow 159=3\times 53$
It does not contain 8 as its factor.
$\therefore$ the number 12159 is not divisible by 8.
F. 14560
We here have the number 14560 with us.
Its last 2 digits are 60.
We know that:-
$\Rightarrow 60=4\times 15$
$\therefore$ the number 14560 is divisible by 4.
Its last 3 digits are 560.
We know that:-
$\Rightarrow 560=8\times 70$
$\therefore$ the number 14560 is divisible by 8.
G. 21084
We here have the number 21084 with us.
Its last 2 digits are 84.
We know that:-
$\Rightarrow 84=4\times 21$
$\therefore$ the number 21084 is divisible by 4.
Its last 3 digits are 084 that is 84.
We know that:-
$\Rightarrow 84=2\times 2\times 3\times 7$
It does not have 8 as a factor.
$\therefore$ the number 21084 is not divisible by 8.
H. 31795072
We here have the number 31795072 with us.
Its last 2 digits are 72.
We know that:-
$\Rightarrow 72=4\times 18$
$\therefore$ the number 31795072 is divisible by 4.
Its last 3 digits are 072 that is 72.
We know that:-
$\Rightarrow 72=8\times 9$
$\therefore$ the number 31795072 is divisible by 8.
I. 1700
We here have the number 1700 with us.
Its last 2 digits are 00.
0 is definitely divisible by 4.
$\therefore$ the number 1700 is divisible by 4.
Its last 3 digits are 700.
We know that:-
$\Rightarrow 700=2\times 2\times 5\times 5\times 7$
It does not have 8 as a factor.
$\therefore$ the number 1700 is not divisible by 8.
J. 2150
We here have the number 2150 with us.
Its last 2 digits are 50.
We know that:-
$\Rightarrow 50=2\times 5\times 5$
$\therefore$ the number 2150 is not divisible by 4.
Now since 2150 does not have 4 as a factor, it cannot have 8 as well.
$\therefore$ the number 2150 is not divisible by 8.

Note: The students must know the divisibility rules for the numbers to be divisible by 4 or 8 as follows:-
Divisibility by 4: If the number formed by the last two digits of the number is divisible by 4, then we say that the number is divisible by 4.
Divisibility by 8: If the number formed by the last three digits of the number is divisible by 8, then we say that the number is divisible by 8.