Mathematics
Fundamental Theorem of Arithmetic
अंकगणित का मौलिक प्रमेय
In this Class 10 Mathematics topic from the chapter Real Numbers, students learn that every integer greater than 1 can be expressed as a product of prime numbers, and that this prime factorisation is unique apart from the order of the factors. They practise finding prime factors and use the theorem to understand and determine the HCF and LCM of numbers. The topic builds clear reasoning about the structure of whole numbers and supports later work with divisibility and number relationships.
Practice questions
According to the Fundamental Theorem of Arithmetic, every composite number can be written in which form?EasyLevel 4What is the prime factorisation of 36?EasyLevel 4What is the correct prime factorisation of 60?EasyLevel 4What does uniqueness mean in the Fundamental Theorem of Arithmetic?EasyLevel 4In the prime factorisation of 84, what is the power of 2?EasyLevel 4The number (2^3\times3^2) is equal to which number?EasyLevel 4Which is the prime factorisation of 45?EasyLevel 4Which of the following numbers is prime?EasyLevel 4Which of the following numbers is composite?EasyLevel 4What is the prime factorisation of 90?EasyLevel 4If (72=2^3\times3^2), how many distinct prime factors does 72 have?EasyLevel 4Which is the prime factorisation of 100?EasyLevel 4If two numbers have prime factorisations (2^2\times3) and (2\times3^2), what is their HCF?EasyLevel 4If two numbers have prime factorisations (2^2\times3) and (2\times3^2), what is their LCM?EasyLevel 4What is the prime factorisation of 144?EasyLevel 4What is the value of (3^2\times5)?EasyLevel 4How should the factors be in a prime factorisation?EasyLevel 4Which is the prime factorisation of 75?EasyLevel 4Which prime factors appear in the prime factorisation of 56?EasyLevel 4What is the HCF of two co-prime numbers?EasyLevel 4