Let me ask a question. Please explain the way to find the answer? here comes the question
in each of the following, without actual division and by using divisibility tests find whether the first number is divisible by the second number:
A) 6245 by 45
B) 77496 by 12
C) 317925 by 15
D) 76806849 by 18
Answer :
We can check without actual division and by using divisibility tests these number is divisible by second number or not
A ) we have 6245 by 45 ( )
First we make prime factors of denominator As : 45 = 3 3 5 , So if our number is divisible by 3 and 5 , so our number is also divisible by 45 ,
And
we know Divisiblity rule for 3 :
Add up all of the digits in the number. If the sum of the digits is divisible by 3, then so is the number.
So 6245 = 6 + 2 + 4 + 5 = 17 that is not divisible by 3 so 6245 also not divisible by 3
So,
6245 is not divisible by 45 also. ( Ans )
B ) 77496 by 12 ( )
First we make prime factors of denominator As : 12 = 2 2 3 , So if our number is divisible by 2 and 3 , so our number is also divisible by 12 ,
And
We know
Division by 2:
If the number ends in 0, 2, 4, 6, or 8, then the number is divisible by 2. This is equivalent to being an even number.
So our number 77496 is divisible by 2
And
we know Divisibility rule for 3 :
Add up all of the digits in the number. If the sum of the digits is divisible by 3, then so is the number.
So 77496 = 7 + 7 + 4 + 9 + 6 = 33 that is divisible by 3 so 77496 also divisible by 3
So,
77496 is divisible by 12 also . ( Ans )
C ) 317925 by 15 ( )
First we make prime factors of denominator As : 15 = 3 5 , So if our number is divisible by 3 and 5 , so our number is also divisible by 15 ,
we know Divisibility rule for 3 :
Add up all of the digits in the number. If the sum of the digits is divisible by 3, then so is the number.
So , 317925 = 3 + 1 + 7 + 9 + 2 + 5 = 27 that is divisible by 3 so 317925 also divisible by 3
And
Division by 5:
If the last digit is 0 or 5 then the number can be divided by 5.
Our number 317925 is divisible by 5 , as last digit is ' 5 '
So,
317925 is divisible by 15 also . ( Ans )
D ) 76806849 by 18 ( )
First we make prime factors of denominator As : 18 = 2 3 3 , So if our number is divisible by 2 and 3 , so our number is also divisible by 18 ,
And
We know
Division by 2:
If the number ends in 0, 2, 4, 6, or 8, then the number is divisible by 2. This is equivalent to being an even number.
So our number 76806849 is not divisible by 2 as its last digit is ' 9 '
So,
76806849 is not divisible by 18 also . ( Ans )
We can check without actual division and by using divisibility tests these number is divisible by second number or not
A ) we have 6245 by 45 ( )
First we make prime factors of denominator As : 45 = 3 3 5 , So if our number is divisible by 3 and 5 , so our number is also divisible by 45 ,
And
we know Divisiblity rule for 3 :
Add up all of the digits in the number. If the sum of the digits is divisible by 3, then so is the number.
So 6245 = 6 + 2 + 4 + 5 = 17 that is not divisible by 3 so 6245 also not divisible by 3
So,
6245 is not divisible by 45 also. ( Ans )
B ) 77496 by 12 ( )
First we make prime factors of denominator As : 12 = 2 2 3 , So if our number is divisible by 2 and 3 , so our number is also divisible by 12 ,
And
We know
Division by 2:
If the number ends in 0, 2, 4, 6, or 8, then the number is divisible by 2. This is equivalent to being an even number.
So our number 77496 is divisible by 2
And
we know Divisibility rule for 3 :
Add up all of the digits in the number. If the sum of the digits is divisible by 3, then so is the number.
So 77496 = 7 + 7 + 4 + 9 + 6 = 33 that is divisible by 3 so 77496 also divisible by 3
So,
77496 is divisible by 12 also . ( Ans )
C ) 317925 by 15 ( )
First we make prime factors of denominator As : 15 = 3 5 , So if our number is divisible by 3 and 5 , so our number is also divisible by 15 ,
we know Divisibility rule for 3 :
Add up all of the digits in the number. If the sum of the digits is divisible by 3, then so is the number.
So , 317925 = 3 + 1 + 7 + 9 + 2 + 5 = 27 that is divisible by 3 so 317925 also divisible by 3
And
Division by 5:
If the last digit is 0 or 5 then the number can be divided by 5.
Our number 317925 is divisible by 5 , as last digit is ' 5 '
So,
317925 is divisible by 15 also . ( Ans )
D ) 76806849 by 18 ( )
First we make prime factors of denominator As : 18 = 2 3 3 , So if our number is divisible by 2 and 3 , so our number is also divisible by 18 ,
And
We know
Division by 2:
If the number ends in 0, 2, 4, 6, or 8, then the number is divisible by 2. This is equivalent to being an even number.
So our number 76806849 is not divisible by 2 as its last digit is ' 9 '
So,
76806849 is not divisible by 18 also . ( Ans )