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^{12}\times3^9\times5^4\times7^3\times17), how many distinct prime factors does it have?ExpertLevel 6If the two numbers are (2^9\times3^5\times13) and (5^6\times7^4\times11), which statement about them is correct?ExpertLevel 6If the product of two co-prime numbers is 12673, what is their LCM?ExpertLevel 6What is the prime factorisation of 131072?ExpertLevel 6Which is the prime factorisation of 2822400?ExpertLevel 6If (n=2^8\times3^7\times5^4\times23), by which number must (n) be divisible?ExpertLevel 6If (n=2^{10}\times3^6\times5^4), by which of the following will (n) not be divisible?ExpertLevel 6Which option gives the correct value of (2^{11}\times3^5\times5)?ExpertLevel 6If the prime factorisation of a number is (2^7\times3^6\times5^3), what is the number?ExpertLevel 6If (a=2^7\times3^8\times7) and (b=2^{10}\times3^5\times7^6), what is the power of 2 in the LCM of (a) and (b)?ExpertLevel 6If (a=2^7\times3^8\times7) and (b=2^{10}\times3^5\times7^6), what is the power of 7 in the HCF of (a) and (b)?ExpertLevel 6Which is the prime factorisation of 524880?ExpertLevel 6If a number has prime factorisation (2^{12}\times3^8\times5^5), what is the smallest number by which it must be multiplied to make a perfect cube?ExpertLevel 6By which smallest number should 254016 be divided to get a perfect square?ExpertLevel 6If (x=2^8\times3^5\times7^6) and (y=2^6\times5^4\times7^7), what will be the power of 7 in (xy)?ExpertLevel 6If (x=2^{10}\times3^6\times5) and (y=2^9\times3^3\times11^2), what will be the power of 2 in (xy)?ExpertLevel 6Which option gives all distinct prime factors of 223092870 correctly?ExpertLevel 6If (a=2^8\times3^5\times17^2) and (b=2^6\times3^7\times5^2\times17), what is the HCF of (a) and (b)?ExpertLevel 6If (a=2^8\times3^5\times17^2) and (b=2^6\times3^7\times5^2\times17), which is the LCM of (a) and (b)?ExpertLevel 6If the HCF of two numbers is 720 and their LCM is 100800, what is the power of 2 in their product?ExpertLevel 6