Fill in the blanks :
(i) All the factors of 20 are ...............
(ii) L.C.M. of two numbers =
(iii) If H.C.F. of two numbers is 1, then these numbers are called ............... .
(iv) Is 65781 divisible by 9 ? ............... .
(v) Write the smallest number having three different prime factors. ...............
Answer
(i) We have,
20 = 1 × 20
20 = 2 × 10
20 = 4 × 5
All the factors of 20 are 1, 2, 4, 5, 10, 20 .
(ii) L.C.M. of two numbers =
(iii) If H.C.F. of two numbers is 1, then these numbers are called co-primes.
(iv) Yes, 65781 is divisible by 9. Because, the sum of the digits of 65781 is,
6 + 5 + 7 + 8 + 1 = 27
Since the sum of its digits 27 is divisible by 9, 65781 is also divisible by 9.
(v) The smallest three prime numbers are 2, 3 and 5.
2 × 3 × 5 = 30,
So the smallest number having three different prime factors is 30.
Write (T) for true and (F) for false for each of the statements given below :
(i) 1 is the smallest prime number.
(ii) A prime number has exactly two factors.
(iii) Two numbers are co-prime only when their H.C.F. is 1.
(iv) Every number is a multiple of itself.
(v) If a and b are co-prime, then their L.C.M. is ab.
(vi) The smallest number of 4 digits exactly divisible by 2, 3 and 5 is 1020.
Answer
(i) The statement is F. 2 is the smallest prime; 1 is neither prime nor composite.
(ii) The statement is T. A prime number is divisible only by 1 and itself.
(iii) The statement is T. If the H.C.F. of two numbers is 1, then the two numbers have no common factors other than 1, which defines co-prime numbers.
(iv) The statement is T. Any number multiplied by 1 gives itself.
(v) The statement is T. If and are co-primes, their H.C.F. is 1. For any two numbers and , L.C.M. = .
(vi) The statement is T. L.C.M. of 2, 3 and 5 = 2 × 3 × 5 = 30, and the smallest 4-digit multiple of 30 = 30 × 34 = 1020.