Real Numbers

Question

The sets of Physics, Chemistry and Mathematics books have to be stacked in such a way that all the books are stored topic wise and the height of each stack is the same. The number of Physics books is 12, the number of Chemistry books 20 and the number of Mathematics books is 30. Assuming that the books are of the same thickness, determine the number of stacks of Physics, Chemistry and Mathematics books.

Solution

In order to arrange the books as required, we have to find the largest number that divides 12, 20 and30 exactly. Clearly, we have to find HCF. Now,

Since, 12 = 2 × 2 × 3 = 2² × 3

20 = 2 × 2 × 5 = 2² × 5

and 30 = 2 × 3 × 5

HCF = Product of common prime factors with lowest powers

= 2

So, there must be 2 books in each stack.

∴ Number of stacks of Physics books
$equals 12 over 2 equals 6$
Number of stacks of Chemistry books
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Number of stacks of Mathematics books
$equals 30 over 2 equals 15$

Some More Questions From Real Numbers Chapter

Use Euclid’s division algorithm to find the HCF of:
(i)135 and 225 (ii) 196 and 38220.

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

Some More Questions From Real Numbers Chapter

Use Euclid’s division algorithm to find the HCF of:
(i)135 and 225 (ii) 196 and 38220.

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

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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For Daily Free Study Material Join wiredfaculty

Real Numbers

Some More Questions From Real Numbers Chapter

Use Euclid’s division algorithm to find the HCF of: (i)135 and 225 (ii) 196 and 38220.

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

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Use Euclid’s division algorithm to find the HCF of:
(i)135 and 225 (ii) 196 and 38220.