Theorems and Laws [1]
The Fundamental Theorem of Arithmetic
Statement:
Every composite number can be expressed (factorised) as a product of primes, and this factorisation is unique, apart from the order in which the prime factors occur.
Important Questions [20]
- Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers.
- What is the Hcf of Smallest Prime Number and the Smallest Composite Number ?
- Find HCF and LCM of 404 and 96 and verify that HCF × LCM = Product of the two given numbers.
- The ratio of LCM and HCF of the least composite and the least prime numbers is ______.
- Show the 6n cannot end with digit 0 for any natural number 'n'.
- Find the HCF and LCM of 72 and 120.
- Find the HCF and LCM of 26, 65 and 117, using prime factorisation.
- The LCM of smallest 2-digit number and smallest composite number is ______.
- Two numbers are in the ratio 2 : 3 and their LCM is 180. What is the HCF of these numbers?
- (HCF × LCM) for the numbers 70 and 40 is ______.
- Read the following passage: Khushi wants to organize her birthday party. Being health conscious, she decided to serve only fruits in her birthday party. She bought 39 apples
- (HCF × LCM) for the numbers 30 and 70 is ______.
- If HCF (72, 120) = 24, then LCM (72, 120) is ______.
- The prime factorisation of the number 2304 is ______.
- If n is a natural number, then 8n cannot end with digit
- The HCF of the smallest 2-digit number and the smallest composite number is ______.
- The mean of first ten natural numbers is ______.
- The prime factorisation of the number 5488 is ______.
- Three bells toll at intervals of 9, 12 and 15 minutes respectively. If they start tolling together, after what time will they next toll together?
- The HCF of two numbers 65 and 104 is 13. If LCM of 65 and 104 is 40x, then the value of x is ______.
Concepts [2]
- Fundamental Theorem of Arithmetic
- Revisiting Irrational Numbers
