List of top Mathematics Questions on The Fundamental Theorem of Arithmetic

Assertion (A) : H.C.F. ($36\text{ m}^2, 18\text{ m}$) = $18\text{ m}$, where m is a prime number.
Reason (R) : H.C.F. of two numbers is always less than or equal to the smaller number.

For any natural number $n$, $6^n$ ends with the digit :

For any natural number n, \(5^n\) ends with the digit :

For any natural number $n$, $6^n$ ends with the digit :

Find the H.C.F. and L.C.M. of 408 and 312.

\(17 \times 11 \times 13 + 11\) is

If H.C.F. of \(135x^2\) and \(189x^3\) is 108, then find the value of x.

There is a circular path around a sports field. Sonia takes \(18\) minutes to drive one round of the field, while Ravi takes \(12\) minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point?

Explain why \(7 × 11 × 13 + 13\) and  \(7 × 6 × 5 × 4 × 3 × 2 × 1 + 5\) are composite numbers.

Check whether \(6n\) can end with the digit \(0\) for any natural number \(n\).

Given that HCF \((306, 657) = 9\) , find LCM \((306, 657)\).

Find the LCM and HCF of the following integers by applying the prime factorisation method. 

1. \(12, 15\) and 
2.  \(17, 23\) and 
3. \(8, 9\) and \(25\)

Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers.

1. \(26\) and \(91\)
2. \(510\) \(\)and \(92\)
3. \(336\) and \(54\)

Express each number as a product of its prime factors: 

1. \(140\) 
2. \(156\) 
3. \(3825\) 
4. \(5005\) 
5. \(7429\)