Divisibility rule of 93 example

1. Check whether 24645 is divisible by 93 or not?

Solution:

Divisibility rule of 93 :
28 times the last digit and add it to the rest of the number.
If the answer is divisible by 93, then number is also divisible by 93.
(Apply this rule to the answer again if necessary)

24645⇒2464+5×28=2464+140=2604 $2464color{red}{5}=>2464 + color{red}{5} xx 28 = 2464 +140 = 2604$

2604⇒260+4×28=260+112=372 $260color{red}{4}=>260 + color{red}{4} xx 28 = 260 +112 = 372$

372⇒37+2×28=37+56=93 $37color{red}{2}=>37 + color{red}{2} xx 28 = 37 +56 = 93$

Here 93 is divisible by 93.

$:.$ 24645 is divisible by 93.

Method-2 :

Divisibility rule of 93 :
If number is divisible by 3 and 31, then number is also divisible by 93.

Divisibility rule of 3 :
The sum of the digits is divisible by 3, then number is also divisible by 3.

Sum of digits of 24645 is

$2+4+6+4+5=21$ , which is divisible by 3.

$:.$ 24645 is divisible by 3.

Divisibility rule of 31 :
3 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 31, then number is also divisible by 31.
(Apply this rule to the answer again if necessary)

$2464color{red}{5}=>2464 - color{red}{5} xx 3 = 2464 -15 = 2449$

$244color{red}{9}=>244 - color{red}{9} xx 3 = 244 -27 = 217$

$21color{red}{7}=>21 - color{red}{7} xx 3 = 21 -21 = 0$

Here 0 is divisible by 31.

$:.$ 24645 is divisible by 31.

24645 is divisible by 3 and 31.

$:.$ 24645 is divisible by 93.

2. Check whether 29109 is divisible by 93 or not?

Solution:

$2910color{red}{9}=>2910 + color{red}{9} xx 28 = 2910 +252 = 3162$

$316color{red}{2}=>316 + color{red}{2} xx 28 = 316 +56 = 372$

$37color{red}{2}=>37 + color{red}{2} xx 28 = 37 +56 = 93$

Here 93 is divisible by 93.

$:.$ 29109 is divisible by 93.

Method-2 :

Divisibility rule of 93 :
If number is divisible by 3 and 31, then number is also divisible by 93.

Divisibility rule of 3 :
The sum of the digits is divisible by 3, then number is also divisible by 3.

Sum of digits of 29109 is

$2+9+1+0+9=21$ , which is divisible by 3.

$:.$ 29109 is divisible by 3.

$2910color{red}{9}=>2910 - color{red}{9} xx 3 = 2910 -27 = 2883$

$288color{red}{3}=>288 - color{red}{3} xx 3 = 288 -9 = 279$

$27color{red}{9}=>27 - color{red}{9} xx 3 = 27 -27 = 0$

Here 0 is divisible by 31.

$:.$ 29109 is divisible by 31.

29109 is divisible by 3 and 31.

$:.$ 29109 is divisible by 93.

3. Check whether 37014 is divisible by 93 or not?

Solution:

$3701color{red}{4}=>3701 + color{red}{4} xx 28 = 3701 +112 = 3813$

$381color{red}{3}=>381 + color{red}{3} xx 28 = 381 +84 = 465$

$46color{red}{5}=>46 + color{red}{5} xx 28 = 46 +140 = 186$

$18color{red}{6}=>18 + color{red}{6} xx 28 = 18 +168 = 186$

Here 186 is divisible by 93.

$:.$ 37014 is divisible by 93.

Method-2 :

Divisibility rule of 93 :
If number is divisible by 3 and 31, then number is also divisible by 93.

Divisibility rule of 3 :
The sum of the digits is divisible by 3, then number is also divisible by 3.

Sum of digits of 37014 is

$3+7+0+1+4=15$ , which is divisible by 3.

$:.$ 37014 is divisible by 3.

$3701color{red}{4}=>3701 - color{red}{4} xx 3 = 3701 -12 = 3689$

$368color{red}{9}=>368 - color{red}{9} xx 3 = 368 -27 = 341$

$34color{red}{1}=>34 - color{red}{1} xx 3 = 34 -3 = 31$

Here 31 is divisible by 31.

$:.$ 37014 is divisible by 31.

37014 is divisible by 3 and 31.

$:.$ 37014 is divisible by 93.

4. Check whether 25406 is divisible by 93 or not?

Solution:

$2540color{red}{6}=>2540 + color{red}{6} xx 28 = 2540 +168 = 2708$

$270color{red}{8}=>270 + color{red}{8} xx 28 = 270 +224 = 494$

$49color{red}{4}=>49 + color{red}{4} xx 28 = 49 +112 = 161$

$16color{red}{1}=>16 + color{red}{1} xx 28 = 16 +28 = 44$

Here 44 is not divisible by 93.

$:.$ 25406 is not divisible by 93.

Method-2 :

Divisibility rule of 93 :
If number is divisible by 3 and 31, then number is also divisible by 93.

Divisibility rule of 3 :
The sum of the digits is divisible by 3, then number is also divisible by 3.

Sum of digits of 25406 is

$2+5+4+0+6=17$ , which is not divisible by 3.

$:.$ 25406 is not divisible by 3.

Hence 25406 is also not divisible by 93.

5. Check whether 28942 is divisible by 93 or not?

Solution:

$2894color{red}{2}=>2894 + color{red}{2} xx 28 = 2894 +56 = 2950$

$295color{red}{0}=>295 + color{red}{0} xx 28 = 295 = 295$

$29color{red}{5}=>29 + color{red}{5} xx 28 = 29 +140 = 169$

$16color{red}{9}=>16 + color{red}{9} xx 28 = 16 +252 = 268$

Here 268 is not divisible by 93.

$:.$ 28942 is not divisible by 93.

Method-2 :

Divisibility rule of 93 :
If number is divisible by 3 and 31, then number is also divisible by 93.

Divisibility rule of 3 :
The sum of the digits is divisible by 3, then number is also divisible by 3.

Sum of digits of 28942 is

$2+8+9+4+2=25$ , which is not divisible by 3.

$:.$ 28942 is not divisible by 3.

Hence 28942 is also not divisible by 93.

6. Check whether 33248 is divisible by 93 or not?

Solution:

$3324color{red}{8}=>3324 + color{red}{8} xx 28 = 3324 +224 = 3548$

$354color{red}{8}=>354 + color{red}{8} xx 28 = 354 +224 = 578$

$57color{red}{8}=>57 + color{red}{8} xx 28 = 57 +224 = 281$

$28color{red}{1}=>28 + color{red}{1} xx 28 = 28 +28 = 56$

Here 56 is not divisible by 93.

$:.$ 33248 is not divisible by 93.

Method-2 :

Divisibility rule of 93 :
If number is divisible by 3 and 31, then number is also divisible by 93.

Divisibility rule of 3 :
The sum of the digits is divisible by 3, then number is also divisible by 3.

Sum of digits of 33248 is

$3+3+2+4+8=20$ , which is not divisible by 3.

$:.$ 33248 is not divisible by 3.

Hence 33248 is also not divisible by 93.

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93. Divisibility rule of 93 example