Consider the number 12ⁿ, where n is a natural number. Check whether there is any value of n ∊ N for which 12ⁿ ends with the digit zero.

Solution

We know, if any number ends with the digit zero it is always divisible by 5.

⇒ If 12ⁿ ends with the digit zero, it must be divisible by 5.

This is possible only if prime factorisation of 12ⁿ contains the prime number 5.

Now, 12 = 2 × 2 × 3 = 2² × 3

⇒ 12ⁿ = (2² × 3)ⁿ = 2² × 3ⁿ

i.e., prime factorisation of 12' does not contain the prime number 5.

⇒ There is no value of n ∊ N for which 12ⁿ ends with the digit zero.

Some More Questions From Real Numbers Chapter

Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer.

An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?

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Real Numbers

Consider the number 12ⁿ, where n is a natural number. Check whether there is any value of n ∊ N for which 12ⁿ ends with the digit zero.

Some More Questions From Real Numbers Chapter

Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer.

An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?

Use Euclid’s division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m.

Use Euclid’s division lemma to show that the cube of any positive integer is of the form 9m, 9m + 1 or 9m + 8.

Express each number as a product of its prime factors: (i) 140

Express each number as a product of its prime factors: (ii) 156

Express each number as a product of its prime factors: (ii) 156 (iii) 3825 (iv) 5005 (v) 7429

Express each number as a product of its prime factors: (iv) 5005

Express each number as a product of its prime factors: (v) 7429

Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers. (i) 26 and 91

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For Daily Free Study Material Join wiredfaculty

Real Numbers

Consider the number 12n, where n is a natural number. Check whether there is any value of n ∊ N for which 12n ends with the digit zero.

Some More Questions From Real Numbers Chapter

Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer.

An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?

Use Euclid’s division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m.

Use Euclid’s division lemma to show that the cube of any positive integer is of the form 9m, 9m + 1 or 9m + 8.

Express each number as a product of its prime factors: (i) 140

Express each number as a product of its prime factors: (ii) 156

Express each number as a product of its prime factors: (ii) 156 (iii) 3825 (iv) 5005 (v) 7429

Express each number as a product of its prime factors: (iv) 5005

Express each number as a product of its prime factors: (v) 7429

Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers. (i) 26 and 91

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Consider the number 12ⁿ, where n is a natural number. Check whether there is any value of n ∊ N for which 12ⁿ ends with the digit zero.