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
Which is the prime factorisation of 121?EasyLevel 5What are the distinct prime factors of 198?EasyLevel 5If (30=2\times3\times5) and (42=2\times3\times7), what is the HCF of 30 and 42?EasyLevel 5If (30=2\times3\times5) and (42=2\times3\times7), what is the LCM of 30 and 42?EasyLevel 5What is the prime factorisation of 250?EasyLevel 5Which number has prime factorisation (2^3\times7)?EasyLevel 5If the prime factorisation of a number is (2^5\times3), what is the number?EasyLevel 5Which of the following is not a prime factorisation?EasyLevel 5What is the prime factorisation of 176?EasyLevel 5Which statement is correct about the numbers 22 and 35?EasyLevel 5What is the prime factorisation of 256?EasyLevel 5If (84=2^2\times3\times7) and (126=2\times3^2\times7), what is their HCF?EasyLevel 5If (84=2^2\times3\times7) and (126=2\times3^2\times7), what is their LCM?EasyLevel 5Which of the following numbers is divisible by both 3 and 5?EasyLevel 5What is the value of (2^3\times3\times5^2)?EasyLevel 5In the Fundamental Theorem of Arithmetic, prime factorisation is generally considered for numbers starting from which type?EasyLevel 5What is the prime factorisation of 330?EasyLevel 5If the prime factorisation of a number is (2\times5\times11), what is the number?EasyLevel 5What is the correct prime factorisation of 270?EasyLevel 5If two numbers are co-prime, what conclusion follows from the relation between their HCF and LCM?EasyLevel 5