Consecutive Numbers and Alternate Numbers
Here we will learn about the consecutive numbers and alternate
numbers.
Natural numbers come consecutively whereas odd or even numbers
come alternatively.
Consecutive Numbers:
Natural numbers which differ by 1 are called consecutive numbers.
For example: 1, 2, 3, 4, 5, 6, 7, etc. are consecutive numbers.
Alternate Numbers:
Numbers which differ by 2 are called alternate numbers.
For example: 1,3,5,7, etc. are alternate numbers.
Solved examples
1. Write seven consecutive composite numbers less than 100, such that there is no prime number in between them.
Solution:
Seven such consecutive composite numbers are
90, 91, 92, 93, 94, 95, 96.
2. Write all the alternate numbers less than 25.
Solution:
21, 19, 17, 15, 13, 11, 9, 7, 5, 3, 1
3. Find two consecutive composition numbers less than 10, such that there is no prime number between them.
Solution:
First find the composite numbers less than 10.
4, 6, 8 and 9 are the composite numbers less than 10.
Now we need to check the all consecutive pairs;
(i) 4 and 6
5 is the prime number between 4 and 6.
(ii) 6 and 8
7 is the prime number between 6 and 8.
(iii) 8 and 9
There is no prime number between 8 and 9, so this pair satisfies the condition.
Answer: 8 and 9
3. The number 137 is a threedigit number which remains prime number whichever way we arrange its digits. Find other such threedigit prime numbers having the same characteristics.
Solution:
137 is a threedigit number which remains prime number whichever way we arrange its digits.
Let's check
173 is a prime number prime, since there are no common factors other than 1 and 173.
317 is a prime number prime, since there are no common factors other than 1 and 317 .
371 is a prime number prime, since there are no common factors other than 1 and 371 .
713 is a prime number prime, since there are no common factors other than 1 and 713.
731 is a prime number prime, since there are no common factors other than 1 and 731.
Now we have to find three such different threedigit prime numbers which remains prime number whichever way we arrange its digits.
(i) 139
(ii) 199
(iii) 237
The above three numbers are such different threedigit prime numbers which remains prime number whichever way we arrange its digits.
Answer: 139; 199; 237
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4th Grade Math Activities
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