Question

.If 37y5 is exactly divisible by 9 , then the least value of y is ------------.

Answer 1

Answer:

sum of digit must be multiple of 9

3+7+y+5=15+y

y is digit having value between 0 to 9

15+y must have value between 15 to 24

multiple of 9 between 15 to 24 is 18

15+y=18

y=3

Answer 2

$\large\underline\purple{\bold{Solution :- }}$

We know,

• If the sum of digits of the number is divisible by 9, then the number itself is divisible by 9.

Since,

• 37y5 is divisible by 9.

$\rm : \implies \:3 + 7 + y + 5 = 9 \: or \: 18 \: or \: 27 \: or \: ...$

$\rm : \implies \:15 + y = 9 \: or \: 18 \: or \: 27 \: ...$

$\rm : \implies \:15 + y = 18$

$\boxed{ \blue{ \: \rm : \implies \:y \: = \: 3}}$

Explore more :-

• Divisibility rule of 2 states If a number is even or a number whose last digit is an even number i.e.  2,4,6,8 including 0, it is always completely divisible by 2.

• Divisibility rule for 3 states that a number is completely divisible by 3 if the sum of its digits is divisible by 3.

• Divisibility rule for 4 states that If the last two digits of a number are divisible by 4, then that number is a multiple of 4 and is divisible by 4 completely.

• Divisibility rule for 5 states that Numbers, which last with digits, 0 or 5 are always divisible by 5.

• Divisibility rule for 6 states that Numbers which are divisible by both 2 and 3 are divisible by 6. That is, if the last digit of the given number is even and the sum of its digits is a multiple of 3, then the given number is also a multiple of 6.

• Divisibility rule for 8 states that If the last three digits of a number are divisible by 8, then the number is completely divisible by 8.

• Divisibility rule for 11 states that If the difference of the sum of alternative digits of a number is divisible by 11, then that number is divisible by 11 completely.