Is 1890 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 1890 is composite or not first we have to find its factors.
Factors of 1890:
- If we have taken numbers from 1, 2, 3…for checking factors of 1890, we found that 1890 has factors 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 27, 30, 35, 42, 45, 54, 63, 70, 90, 105, 126, 135, 189, 210, 270, 315, 378, 630, 945 and 1890. Hence, we must say that 1890 is a composite number.
- Thus, 1890 is the composite number.
- If we multiply 1890 by 1, 2, 3 then we get the multiples of 1890 which are 1890, 3780 and so on.
About the number 1890:
- 1890 has more than two factors which are 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 27, 30, 35, 42, 45, 54, 63, 70, 90, 105, 126, 135, 189, 210, 270, 315, 378, 630, 945 and 1890 and hence it is the composite number.
- 1890 is the even composite number and it is not the perfect square also.
- If we divide 1890 by, 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 27, 30, 35, 42, 45, 54, 63, 70, 90, 105, 126, 135, 189, 210, 270, 315, 378, 630, 945 and 1890 then we get remainder as zero. Hence, 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 27, 30, 35, 42, 45, 54, 63, 70, 90, 105, 126, 135, 189, 210, 270, 315, 378, 630, 945 and 1890 are the factors of 1890.
Note:
- 1890 is not the perfect square.
- Factors of 1890: 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 27, 30, 35, 42, 45, 54, 63, 70, 90, 105, 126, 135, 189, 210, 270, 315, 378, 630, 945 and 1890
- Prime factors of 1890: 2, 3, 5, 7
Conclusion:
- 1890 is the composite number which has factors 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 27, 30, 35, 42, 45, 54, 63, 70, 90, 105, 126, 135, 189, 210, 270, 315, 378, 630, 945 and 1890
- And hence, 1890 is not the prime number.
Multiple Choice Questions:
1) 1890 is a
a) Prime number
b) Odd number
c) Composite number
d) Both a and c
Ans: c) composite number
2) The non-prime factors of a composite number 1890 are
a) 1890
b) 2, 3, 5, 7
c) 1, 6, 9, 10, 14, 15, 18, 21, 27, 30, 35, 42, 45, 54, 63, 70, 90, 105, 126, 135, 189, 210, 270, 315, 378, 630, 945 and 1890
d) 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 27, 30, 35, 42, 45, 54, 63, 70, 90, 105, 126, 135, 189, 210, 270, 315, 378, 630, 945 and 1890
Ans: c) 1, 6, 9, 10, 14, 15, 18, 21, 27, 30, 35, 42, 45, 54, 63, 70, 90, 105, 126, 135, 189, 210, 270, 315, 378, 630, 945 and 1890
3) 1890 is composite number because
a) It has factors 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 27, 30, 35, 42, 45, 54, 63, 70, 90, 105, 126, 135, 189, 210, 270, 315, 378, 630, 945 and 1890
b) It has only two factors
c) Divisible by 2
d) Both a and c
Ans: a) it has factors 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 27, 30, 35, 42, 45, 54, 63, 70, 90, 105, 126, 135, 189, 210, 270, 315, 378, 630, 945 and 1890