Page 48 - Revised Maths Wisdom Class - 6

46 MATHS

Example 5: Find the smallest and the greatest digit ‘a’ such that 843a6 is divisible by 6.
Solution: Given number = 843a6
Its ones place digit is 6 which is divisible by 2
Now sum of its digit = 8 + 4 + 3 + 6 + a = 21 + a
Remember!er!
21 is divisible by 3 Rememb
Hence the smallest digit is 0. › We can replace an unknown digit by
digits from 0 to 9. So far the smallest
21 + 9 = 30 is divisible by 3 digit starts from 0 and for greatest we
Hence, the greatest digit is 9. should try from 9, 8, ... etc.

To find whether a given number is prime or not

We often get stuck while finding whether a given number is prime or not. To make it easy let us learn and
remember the following rules:
Rule 1: If the given number is not divisible by anyone of the prime numbers less than 15, then it is a prime
number otherwise it is not a prime number.
For example, to check whether 193 is a prime number or not we check its divisibility by all prime
numbers less than 15, i.e., 2, 3, 5, 7, 11 and 13. Since it is not divisible by any one of these prime
numbers, it is a prime number.
Rule 2: If the given number is not divisible by any one of the prime numbers less than 20 (20 × 20 = 400), then
it is a prime number otherwise it is not.
Now try whether 337 is prime number or not.

ILLUSTRATIONS

Example: Which of the following numbers are prime?
(a) 177 (b) 283 (c) 391

Solution: (a) Here 177 < 14 × 14 (b) Here 283 < 17 × 17
So, we check divisibility by 2, 3, 5, 7, 11 and 13. So, we check divisibility by

177 is not divisible by 2 but divisible by 3 2, 3, 5, 7, 11, 13.

Hence it is not a prime number. Since it is not divisible by
any of these prime numbers,
(c) Here 391 < 20 × 20 Hence, it is a prime number.
So, we check divisibility by 2, 3, 5, 7, 11, 13, 17 and 19
Since 391 ÷ 17 = 23. Hence it is not a prime number.

Exercise 3C
Exercise 3C
1. Find the factors of the following numbers using factor tree:
(a) 63 (b) 312 (c) 89 (d) 95

2. Find all the factors of the following numbers using prime factorisation:
(a) 1000 (b) 234 (c) 834 (d) 194 (e) 377
3. Write down the predecessor of the largest 3-digit number and do its prime factorisation.
4. Make all the possible factor trees of 150.