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Subjects

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 720?MediumLevel 6Which is the prime factorisation of 924?MediumLevel 6What is the correct prime factorisation of 1176?MediumLevel 6If (a=2^5\times3^2\times5) and (b=2^3\times3\times5^2\times7), what is the HCF of (a) and (b)?MediumLevel 6If (a=2^5\times3^2\times5) and (b=2^3\times3\times5^2\times7), what is the LCM of (a) and (b)?MediumLevel 6If the product of two numbers is 2520 and their HCF is 21, what is their LCM?MediumLevel 6If the HCF of two numbers is 24 and their LCM is 360, what is their product?MediumLevel 6If (x=2^4\times3^2\times7), what is the value of (x)?MediumLevel 6What is the power of 2 in the prime factorisation of 2520?MediumLevel 6What is the correct prime factorisation of 1575?MediumLevel 6Which number has prime factorisation (2^4\times3^2\times5)?MediumLevel 6If (m=2^3\times3^2\times7\times11), how many distinct prime factors does (m) have?MediumLevel 6If the two numbers are 27 and 64, which statement about them is correct?MediumLevel 6If two numbers are co-prime and their product is 391, what is their LCM?MediumLevel 6Which option shows only prime factorisation?MediumLevel 6If (144=2^4\times3^2) and (168=2^3\times3\times7), what is the HCF of 144 and 168?MediumLevel 6If (144=2^4\times3^2) and (168=2^3\times3\times7), what is the LCM of 144 and 168?MediumLevel 6What is the prime factorisation of 1890?MediumLevel 6If the prime factorisation of a number is (2^6\times3^2), what is the number?MediumLevel 6In (2^5\times3^3\times7), how many prime factors are there if repetition is counted?MediumLevel 6