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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

If the prime factorisation of a number is (2^a\times3^2\times5) and the number is 180, what is the value of (a)?MediumLevel 6If the prime factorisation of a number is (2^3\times3^b\times7) and the number is 1512, what is the value of (b)?MediumLevel 6Which statement is correct about the two numbers (2^4\times7) and (3^2\times5)?MediumLevel 6If two co-prime numbers are 28 and 45, what is their LCM?MediumLevel 6What is the prime factorisation of 2048?MediumLevel 6If (n=2^2\times3^4\times5), what is the value of (n)?MediumLevel 6Which option gives the correct prime factorisation of 1125?MediumLevel 6If a number has prime factorisation (2^3\times3^2\times7^2), how many prime factors does it have including repetition?MediumLevel 6If (A=2^4\times3^3) and (B=2^2\times3^5), what is the HCF of (A) and (B)?MediumLevel 6If (A=2^4\times3^3) and (B=2^2\times3^5), what is the LCM of (A) and (B)?MediumLevel 6What are the distinct prime factors of 1365?MediumLevel 6If the HCF of two numbers is 28 and their LCM is 420, what is their product?MediumLevel 6If the product of two numbers is 5040 and their LCM is 360, what is their HCF?MediumLevel 6What is the prime factorisation of 3375?MediumLevel 6Which option gives the correct understanding about 1?MediumLevel 6If (p=2^3\times3^2\times5) and (q=2^2\times3\times7^2), what is the HCF of (p) and (q)?MediumLevel 6If (p=2^3\times3^2\times5) and (q=2^2\times3\times7^2), what is the LCM of (p) and (q)?MediumLevel 6Which is the prime factorisation of 2772?MediumLevel 6Which conclusion correctly follows from the Fundamental Theorem of Arithmetic?MediumLevel 6If (r=2^5\times3^2\times5^2), what is the value of (r)?MediumLevel 6