12. I am the smallest number, having four different prime factors. Can you find me?
10. Determine if 25110 is divisible by 45.
[Hint : 5 and 9 are co-prime numbers. Test the divisibility of the number by 5 and 9].
9. In which of the following expressions, prime factorisation has been done?
(a) 24 = 2 3 4 (b) 56 = 7 2 2 2
(c) 70 = 2 5 7 (d) 54 = 2 3 9
8. The sum of two consecutive odd numbers is divisible by 4. Verify this statement with the help of some examples.
7. The product of three consecutive numbers is always divisible by 6. Verify this statement with the help of some examples.
6. Find all the prime factors of 1729 and arrange them in ascending order. Now state the relation, if any; between two consecutive prime factors.
5. Write the smallest 5-digit number and express it in the form of its prime factors.
4. Write the greatest 4-digit number and express it in terms of its prime factors.
3. Which factors are not included in the prime factorisation of a composite number?
2. Here are two different factor trees for 60. Write the missing numbers.
1. Which of the following statements are true?
(a) If a number is divisible by 3, it must be divisible by 9.
(b) If a number is divisible by 9, it must be divisible by 3.
(c) A number is divisible by 18, if it is divisible by both 3 and 6.
(d) If a number is divisible by 9 and 10 both, then it must be divisible by 90.
(e) If two numbers are co-primes, at least one of them must be prime.
(f) All numbers which are divisible by 4 must also be divisible by 8.
(g) All numbers which are divisible by 8 must also be divisible by 4.
(h) If a number exactly divides two numbers separately, it must exactly divide their sum.
(i) If a number exactly divides the sum of two numbers, it must exactly divide the two numbers separately