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 three-digit number which remains prime number whichever way we arrange its digits. Find other such three-digit prime numbers having the same characteristics.
Solution:
137 is a three-digit 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 three-digit 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 three-digit 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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