Is 2730 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 2730 is composite or not first we have to find its factors.
Factors of 2730:
- If we have taken numbers from 1, 2, 3…for checking factors of 2730, we found that 2730 has factors 1, 2, 3, 5, 6, 7, 10, 13, 14, 15, 21, 26, 30, 35, 39, 42, 65, 70, 78, 91, 105, 130, 182, 195, 210, 273, 390, 455, 546, 910, 1365 and 2730. Hence, we must say that 2730 is a composite number.
- Thus, 2730 is the composite number.
- If we multiply 2730 by 1, 2, 3 then we get the multiples of 2730 which are 2730, 5460 and so on.
About the number 2730:
- 2730 has more than two factors which are 1, 2, 3, 5, 6, 7, 10, 13, 14, 15, 21, 26, 30, 35, 39, 42, 65, 70, 78, 91, 105, 130, 182, 195, 210, 273, 390, 455, 546, 910, 1365 and 2730 and hence it is the composite number.
- 2730 is the even composite number and it is not the perfect square also.
- If we divide 2730 by, 1, 2, 3, 5, 6, 7, 10, 13, 14, 15, 21, 26, 30, 35, 39, 42, 65, 70, 78, 91, 105, 130, 182, 195, 210, 273, 390, 455, 546, 910, 1365 and 2730 then we get remainder as zero. Hence, 1, 2, 3, 5, 6, 7, 10, 13, 14, 15, 21, 26, 30, 35, 39, 42, 65, 70, 78, 91, 105, 130, 182, 195, 210, 273, 390, 455, 546, 910, 1365 and 2730 are the factors of 2730.
Note:
- 2730 is not the perfect square.
- Factors of 2730: 1, 2, 3, 5, 6, 7, 10, 13, 14, 15, 21, 26, 30, 35, 39, 42, 65, 70, 78, 91, 105, 130, 182, 195, 210, 273, 390, 455, 546, 910, 1365 and 2730
- Prime factors of 2730: 2, 3, 5, 7, 13
Conclusion:
- 2730 is the composite number which has factors, 1, 2, 3, 5, 6, 7, 10, 13, 14, 15, 21, 26, 30, 35, 39, 42, 65, 70, 78, 91, 105, 130, 182, 195, 210, 273, 390, 455, 546, 910, 1365 and 2730
- And hence, 2730 is not the prime number.
Multiple Choice Questions:
1) 2730 is a
a) Prime number
b) Odd number
c) Composite number
d) Both a and c
Ans: c) composite number
2) The composite factors of a composite number 2730 are
a) 2730
b) 2, 3, 5, 7, 13
c) 6, 10, 14, 15, 21, 26, 30, 35, 39, 42, 65, 70, 78, 91, 105, 130, 182, 195, 210, 273, 390, 455, 546, 910, 1365 and 2730
d) 1, 2, 3, 5, 6, 7, 10, 13, 14, 15, 21, 26, 30, 35, 39, 42, 65, 70, 78, 91, 105, 130, 182, 195, 210, 273, 390, 455, 546, 910, 1365 and 2730
Ans: c) 6, 10, 14, 15, 21, 26, 30, 35, 39, 42, 65, 70, 78, 91, 105, 130, 182, 195, 210, 273, 390, 455, 546, 910, 1365 and 2730
3) 2730 is even composite number because
a) It has factors 1, 2, 3, 5, 6, 7, 10, 13, 14, 15, 21, 26, 30, 35, 39, 42, 65, 70, 78, 91, 105, 130, 182, 195, 210, 273, 390, 455, 546, 910, 1365 and 2730
b) It has only two factors
c) Divisible by 2
d) Both a and c
Ans: d) both a and c