According to class materials, consider the statement, If n is divisible by 30 th

Question

According to class materials, consider the statement, If n is divisible by 30 then n is divisible by 2 and by 3 and by5 to this statement? O 1.(a) If n is not divisible by 30 then n is divisible by 2 or divisible by 3 or divisible by 5. 0 2. (b) If n is not divisible by 30 then n is not divisible by 2 or not divisible by 3 or not divisible by 5. O 3.(c) If n is divisible by 2 and divisible by 3 and divisible by 5 then n is divisible by 30. O 4.(d) If n is not divisible by 2 or not divisible by 3 or not divisible by 5 then n is not divisible by 30 O 5. (e) If n is divisible by 2 or divisible by 3 or divisible by 5 then n is divisible by 30. O 6.( None of (a) through (e) is the correct answer.

Explanation / Answer

Answer is 3.(c) if n is divisible by 2 and divisible by 3 and divisible by 5 then n is divisible by 30.

explanation- if n is divisible by 2 then 2 will be the one of the factor of n.

similarily we can say that 3 and 5 will be also the one of the factor of n.

here according to the option 3(c) 2,3,5 all will be the factor of n.

we can represent any number in the multiplaction of thier factors.

let us consider other factor of n is p.

so now we can write n=2x3x5xp (where p is the other integral factor of n)

    after multiplication n=30xp

any no can be represented in the multiplication of it's unique factor

so we can say that 30 will also be a one of factor n.

or simply n will be divisible by 30.

IMP Note-If any no is devisible by q then q will be a common factor of that no and vice versa also true.

dear student

for more clarification of other options

a) n is not divisible by 30

then we can write n 30 x p

or n 2x3x5xp

here you can clearly observe that if no is not divisible by 30 then it won't be also divisble by 2,3,5 so options 1 and 2 are wrong. similarily you can check other options also.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.