Is 1296 is a composite number or not ?
- As we already know that, the number having factors 1 and the number itself is the prime number.
- And numbers having more than these two factors are the composite numbers.
- To check whether the number 1296 is composite or not first we have to find its factors.
Factors of 1296:
- If we have taken numbers from 1, 2, 3…for checking factors of 1296, we found that 1296 has factors 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 81, 108, 144, 162, 216, 324, 432, 648 and 1296. Hence, we must say that 1296 is a composite number.
- Thus, 1296 is the composite number.
- If we multiply 1296 by 1, 2, 3 then we get the multiples of 1296 which are 1296, 2592and so on.
About the number 1296:
- 1296 has more than two factors which are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 81, 108, 144, 162, 216, 324, 432, 648 and 1296 and hence it is the composite number.
- 1296 is the even composite number and it is the perfect square also.
- If we divide 1296 by 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 81, 108, 144, 162, 216, 324, 432, 648 and 1296 then we get remainder as zero. Hence, 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 81, 108, 144, 162, 216, 324, 432, 648 and 1296 are the factors of 1296.
Note:
- 1296 is the perfect square.
- Factors of 1296: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 81, 108, 144, 162, 216, 324, 432, 648 and 1296
- Prime factors of 1296: 2, 3
Conclusion:
- 1296 is the composite number which has factors1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 81, 108, 144, 162, 216, 324, 432, 648 and 1296
- And hence, 1296 is not the prime number.
Multiple Choice Questions:
1) 1296 is a
a) Even number
b) a perfect square number
c) Composite number
d) all
Ans: d) all
2) The composite factors of a composite number 1296 are
a) 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 81, 108, 144, 162, 216, 324, 432, 648 and 1296
b) 2, 3
c) 1, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 81, 108, 144, 162, 216, 324, 432, 648 and 1296
d) 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 81, 108, 144, 162, 216, 324, 432, 648 and 1296
Ans: a) 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 81, 108, 144, 162, 216, 324, 432, 648 and 1296
3) 1296 is composite number because
a) It has factors1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 81, 108, 144, 162, 216, 324, 432, 648 and 1296
b) It has more than two factors
c) Divisible by 2
d) Both a and b
Ans: d) both a and b