Problem Questions with Answer, Solution | Mathematics - Exercise 2.2: Fundamental Theorem of Arithmetic | 10th Mathematics : UNIT 2 : Numbers and Sequences
Chapter: 10th Mathematics : UNIT 2 : Numbers and Sequences
Exercise 2.2: Fundamental Theorem of Arithmetic
Exercise 2.2
1. For what values of natural number n, 4n can end with the digit 6?
2. If m, n are natural numbers, for what values of m, does 2n ×5m ends in 5?
3. Find the HCF of 252525 and 363636.
4. If 13824 = 2a × 3b then find a and b.
5. If p1x1 × p2x2 × p3x3 × p4x4 = 113400 where p1 , p2 , p3 , p4 are primes in ascending order and x1, x2, x3, x4 are integers, find the value of p1,p2, p3, p4 and x1, x2, x3, x4.
6. Find the LCM and HCF of 408 and 170 by applying the fundamental theorem of arithmetic.
7. Find the greatest number consisting of 6 digits which is exactly divisible by 24,15,36?.
8. What is the smallest number that when divided by three numbers such as 35, 56 and91 leaves remainder 7 in each case?
9. Find the least number that is divisible by the first ten natural numbers.
Answers:
1. Even number
2. No value
3. 10101
4. 9, 3
5. 2,3,5,7 and 3,4,2,1
6. 2040, 34
7. 999720
8. 3647 9. 2520
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