Question

The integer n is the smallest positive multiple of 15 such that every digit of n is either 8 or 0.
Compute
n/120​

Answer 1

Answer:

The integer n is the smallest positive multiple of 15 such that every digit of n is either 8 or 0 is 8880

Step-by-step explanation:

• Prime factors of 15 are 3 and 5.
• Therefore any multiple of 15 must be divisible by 3 and 5.
• As the required number has to be divisible by 5, it should end with 0.
• Also, the given number must be divisible by 3.
• Therefore if you put one 8 or two eights or one 8 and 0 before 0 that is 80 or 880 or 8880 are not divisible by 3.
• Also we want the smallest multiple of 15.
• Therefore the only possibility is 8880.
• This is required number 8880.

Hence the integer n is the smallest positive multiple of 15 such that every digit of n is either 8 or 0 is 8880.

Answer 2

Therefore the value of n/120 is 74.

Given:

The integer 'n' is the smallest positive multiple of 15 such that every digit of 'n' is either 8 or 0.

To Find:

The value of n/120.

Solution:

The answer to the given question can be found easily using this simple approach.

The multiples of 15 will have at least one '0' and one '8' because the multiples of 15 will have either '0' or '5' in the unit's place.

Let us assume the values of 'n' according to digits.

If 'n' is a,

⇒ 1 digit number: Not Possible

⇒ 2 digit number: 80 is only possible which is not divisible by 15.

⇒ 3 digit number: 800 or 880 is possible both are not divisible by 15.

⇒ 4 digit number: 8000 or 8080 or 8800 or 8880 is possible of which 8880 is only divisible by 15.

So '8880' is the required value of 'n' which satisfies the given conditions. ( n = 8880 )

⇒ n/120 = 8880/120 = 74

Therefore the value of n/120 is 74.

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