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 a number has prime factorisation (2^{10}\times3^7\times5^2\times11^3\times13), how many distinct prime factors does it have?ExpertLevel 4If the two numbers are (2^7\times3^3\times11) and (5^4\times7^2\times13), which statement about them is correct?ExpertLevel 4If the product of two co-prime numbers is 4199, what is their LCM?ExpertLevel 4What is the prime factorisation of 32768?ExpertLevel 4Which is the prime factorisation of 176400?ExpertLevel 4If (n=2^6\times3^5\times5^2\times17), by which number must (n) be divisible?ExpertLevel 4If (n=2^8\times3^4\times5^2), by which of the following will (n) not be divisible?ExpertLevel 4Which option gives the correct value of (2^9\times3^4\times5)?ExpertLevel 4If the prime factorisation of a number is (2^5\times3^6\times5^3), what is the number?ExpertLevel 4If (a=2^5\times3^6\times7) and (b=2^8\times3^3\times7^4), what is the power of 2 in the LCM of (a) and (b)?ExpertLevel 4If (a=2^5\times3^6\times7) and (b=2^8\times3^3\times7^4), what is the power of 3 in the HCF of (a) and (b)?ExpertLevel 4Which is the prime factorisation of 131220?ExpertLevel 4If a number has prime factorisation (2^{10}\times3^5\times5^4), what is the smallest number by which it must be multiplied to make a perfect cube?ExpertLevel 4By which smallest number should 63504 be divided to get a perfect square?ExpertLevel 4If (x=2^6\times3^3\times7^4) and (y=2^4\times5^2\times7^5), what will be the power of 7 in (xy)?ExpertLevel 4If (x=2^8\times3^4\times5) and (y=2^7\times3^2\times11), what will be the power of 2 in (xy)?ExpertLevel 4Which option gives all distinct prime factors of 510510 correctly?ExpertLevel 4If (a=2^6\times3^3\times11^2) and (b=2^4\times3^5\times5^2\times11), what is the HCF of (a) and (b)?ExpertLevel 4If (a=2^6\times3^3\times11^2) and (b=2^4\times3^5\times5^2\times11), what is the LCM of (a) and (b)?ExpertLevel 4If the HCF of two numbers is 180 and their LCM is 25200, what is the power of 2 in their product?ExpertLevel 4