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UPSKILL MATH PLUS

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Subjects
Mathematics CBSE
Class 10
Real Numbers
The Fundamental Theroem of Arithmetic

11. Case study based question: Prime factors and HCF

Exercise condition:

5 m.

The school offers you and your two friends the opportunity to purchase a tree sapling in support of Grade X students Planting Activity, which will promote tree planting practices among students and thus improve our environment. There are 32 boys and 30 girls in the Grade X class.

1. What is the minimum number of trees you will acquire for planting trees, so that they can be distributed equally among all students?

2. The fundamental theorem of arithmetic states that:

Every composite number can be expressed as a product of prime numbers
Every prime numbers can be expressed as a product of composite numbers
Every composite number may or may not be expressed as a product of prime numbers
Every prime number may or may not be expressed as a product of composite numbers

3. Find the HCF of \((32, 30)\), using the relationship between HCF and LCM of two numbers:

4. The positive even integer is of the form:

\(2q\)
\(q + 2\)
\(q + 1\)
\(2q + 1\)

5. \(1 \times\ 2 \times\ 3 \times\ 7 \times\ 9 + 2\) is a:

Neither prime nor composite
Composite number
Square number
Prime number

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