Question

which of the numbers 36, 40, 45, 72 can divide into 51768 exactly​

Answer 1

Given :  number 51768

To Find: which of the numbers 36, 40, 45, 72 can divide into 51768 exactly​

Solution:

Number is divisible by 36  if its divisible by 4 and 9

Number is divisible by 72  if its divisible by 8 and 9

Number is divisible by 40  if its divisible by 8 and 5

Number is divisible by 45  if its divisible by 9 and 5

A number is divisible by 5 if unit digit is 0 or 5

51768 has unit  digit 8 hence not divisible by 5

so 51678 is not divisible by 40 and 45

A number is divisible by 9 if sum of its digit is Divisible by 9

51768

5 + 1 + 7 + 6 + 8 = 27 is divisible by  9

Hence 51678 is divisible by 9

A number is divisible by8  if number formed by last 3 digits is divisible by 8

51768

768/ 8 = 96   hence divisible by  8

Hence 51678 is divisible by 8

51678 is divisible by 8 and 9  hence divisible by 72

72 = 36 * 2

So 51678 is also divisible by  36

36 and 72 divide into 51768 exactly​

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Answer 2

Answer:

to check divisibility for the given number 51768 among numbers : 36, 40, 45,72

finding the factors of above numbers

36 = 4 x 9 ; 40 =5 x 8 ; 45 = 5 x 9 ; 72 = 8 x 9

now checking the divisibility test for the factors -

DIVISIBILITY TEST FOR  8 : a number is divisible by 8 if number formed by last 3 digits is divisible by 8. For 51768-

768/8 =96 ,  hence divisible by 8

DIVISIBILITY TEST FOR 9 : a number is divisible if sum of its digits is divisible by 9 . For 51768 -

5+1+7+6+8 = 27,  hence divisible by 9

DIVISIBILITY TEST FOR 5 :  a number is divisible by 5 if unit digit is 0 or 5

For 51768 - unit digit is 8 , hence not divisible .

since , 51768 is not divisible by 5 , therefore 51768 is not divisible by 40 & 45.

since, 51768 is divisible by 8 & 9 , therefore 51768 is divisible by 72

(72 = 36*2 ) and 36.