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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 correct prime factorisation of 945?MediumLevel 5 Which number has prime factorisation (2^3\times3^2\times5)?MediumLevel 5 If (m=2^4\times3\times5), how many distinct prime factors does (m) have?MediumLevel 5 If the two numbers are 16 and 45, which statement about them is correct?MediumLevel 5 If two numbers are co-prime and their product is 221, what is their LCM?MediumLevel 5 Which option shows only prime factorisation?MediumLevel 5 If (72=2^3\times3^2) and (120=2^3\times3\times5), what is the HCF of 72 and 120?MediumLevel 5 If (72=2^3\times3^2) and (120=2^3\times3\times5), what is the LCM of 72 and 120?MediumLevel 5 What is the prime factorisation of 1260?MediumLevel 5 If the prime factorisation of a number is (2^5\times3^2), what is the number?MediumLevel 5 In (2^4\times3^2\times5), how many prime factors are there if repetition is counted?MediumLevel 5 If the prime factorisation of a number is (2^a\times3^2) and the number is 108, what is the value of (a)?MediumLevel 5 If the prime factorisation of a number is (2^a\times3^3) and the number is 216, what is the value of (a)?MediumLevel 5 Which statement is correct about the two numbers (2^3\times5) and (3^2\times7)?MediumLevel 5 If two co-prime numbers are 18 and 35, what is their LCM?MediumLevel 5 What is the prime factorisation of 1024?MediumLevel 5 If (n=3^4\times5^2), what is the value of (n)?MediumLevel 5 Which option gives the correct prime factorisation of 675?MediumLevel 5 If a number has prime factorisation (2^2\times3^3\times5), how many prime factors does it have including repetition?MediumLevel 5 If (A=2^5\times3^2) and (B=2^3\times3^4), what is the HCF of (A) and (B)?MediumLevel 5