What is the least value of ____ so that the number 9274 __ 5 is divisible by 9?
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Tests for Divisibility
What least value should be ...
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What least value should be given to * so that the number 653∗47 is divisible by 11?
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ANSWER
⇒ Divisibility by 11 : A number is divisible by 11 when the sum of the digits at the odd places and the sum of the digits at the even places are either equal or a multiple of 11.
⇒ Let ∗ be x.
∴ Sum of even digits = 4+3+6=13
∴ Sum of odd digits = 7+x+5=12+x
∴ 12+x−13=0
∴ x=1
⇒ 653147 id divisible by 11.
∴ The value of ∗ is 1.
Concept:
Divisible by 2:A number that is even or a number whose last digit is an even number i.e. 0, 2, 4, 6, and 8.
Divisible by 3: The sum of all the digits of the number should be divisible by 3.
Divisible by 4: Number formed by the last two digits of the number should be divisible by 4 or ending with 00.
Divisible by 5: A numbers having 0 or 5 as their ones place digit.
Divisible by 6: A number that is divisible by both 2 and 3.
Divisible by 7:Subtracting twice the last digit of the number from the remaining digits gives a multiple of 7.
Divisible by 8:Number formed by the last three digits of the number should be divisible by 8 or should be ending with 000.
Divisible by 9:The sum of all the digits of the number should be divisible by 9.
Divisible by 10:Any number whose one's place digit is 0.
Divisible by 11: difference of the sums of the alternative digits of a number is divisible by 11.
Divisible by 12:A number that is divisible by both 3 and 4.
Given:
9274__5 is divisible by 9
Find:
What is the least value of ____ so that the number 9274 __ 5 is divisible by 9?
Solution:
Divisibility by 9:Sum of the digits must be divisible by 9
9+2+7+4+5+x =9k
27+x=9k
if k =3
27+x = 27
x=0
Hence, 0 is the smallest value
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