Advertisements
Advertisements
Question
If 56 × 32y is divisible by 18, find the least value of y.
Advertisements
Solution
It is given that, the number 56 × 32y is divisible by 18.
Then, it is also divisible by each factor of 18.
Thus, it is divisible by 2 as well as 3.
Now, the number is divisible by -2, its unit’s digit must be an even number that is 0, 2, 4, 6, Therefore, the least value of y is 0.
Again, the number is divisible by 3 also, sum of its digits is a multiple of 3. i.e. 5 + 6 + x + 3 + 2 + y is a multiple of 3
⇒ 16 + x + y = 0, 3, 6, 9,...
⇒ 16 + x = 18
⇒ x = 2, which is the least value of x.
APPEARS IN
RELATED QUESTIONS
Without performing actual computations, find the quotient when 94 − 49 is divided by
(i) 9
(ii) 5
If sum of the number 985 and two other numbers obtained by arranging the digits of 985 in cyclic order is divided by 111, 22 and 37 respectively. Find the quotient in each case.
Which of the following statement is true?
If a number exactly divides the sum of two numbers, it must exactly divide the numbers separately.
Which of the following statement is true?
If a number divides three numbers exactly, it must divide their sum exactly.
Do you remember magic triangles? Come now, let s make some magic squares.
- Fill this square using all the numbers from 21 to 29.
Rule: The total of each side is 75.
Now you try and change these numbers into special numbers —
28
If a 3-digit number abc is divisible by 11, then ______ is either 0 or multiple of 11.
If A × 3 = 1A, then A = ______.
A three-digit number abc is divisible by 6 if c is an even number and a + b + c is a multiple of 3.
If 148101B095 is divisible by 33, find the value of B.
