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
What is the prime factorisation of 512?EasyLevel 6If (90=2\times3^2\times5) and (150=2\times3\times5^2), what is their HCF?EasyLevel 6If (90=2\times3^2\times5) and (150=2\times3\times5^2), what is their LCM?EasyLevel 6Which of the following numbers is divisible by both 2 and 5?EasyLevel 6What is the value of (2^4\times3\times5^2)?EasyLevel 6What is special about prime factorisation in the Fundamental Theorem of Arithmetic?EasyLevel 6What is the prime factorisation of 462?EasyLevel 6If the prime factorisation of a number is (3\times7\times11), what is the number?EasyLevel 6What is the correct prime factorisation of 540?EasyLevel 6If two numbers are co-prime, their LCM is equal to what?EasyLevel 6What is the correct meaning of uniqueness in the Fundamental Theorem of Arithmetic?MediumLevel 5What is the correct prime factorisation of 540?MediumLevel 5Which is the prime factorisation of 756?MediumLevel 5What is the correct prime factorisation of 980?MediumLevel 5If (a=2^4\times3^2\times5) and (b=2^2\times3^3\times7), what is the HCF of (a) and (b)?MediumLevel 5If (a=2^4\times3^2\times5) and (b=2^2\times3^3\times7), what is the LCM of (a) and (b)?MediumLevel 5If the product of two numbers is 1512 and their HCF is 18, what is their LCM?MediumLevel 5If the HCF of two numbers is 15 and their LCM is 210, what is their product?MediumLevel 5If (x=2^3\times3^2\times7), what is the value of (x)?MediumLevel 5What is the power of 3 in the prime factorisation of 1512?MediumLevel 5