Is 2400 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 2400 is composite or not first we have to find its factors.
Factors of 2400:
- If we have taken numbers from 1, 2, 3…for checking factors of 2400, we found that 2400 has factors 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 75, 80, 96, 100, 120, 150, 160, 200, 240, 300, 400, 480, 600, 800, 1200 and 2400. Hence, we must say that 2400 is a composite number.
- Thus, 2400 is the composite number.
- If we multiply 2400 by 1, 2, 3 then we get the multiples of 2400 which are 2400, 4800 and so on.
About the number 2400:
- 2400 has more than two factors which are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 75, 80, 96, 100, 120, 150, 160, 200, 240, 300, 400, 480, 600, 800, 1200 and 2400 and hence it is the composite number.
- 2400 is the even composite number and it is not the perfect square also.
- If we divide 2400 by, 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 75, 80, 96, 100, 120, 150, 160, 200, 240, 300, 400, 480, 600, 800, 1200 and 2400 then we get remainder as zero. Hence, 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 75, 80, 96, 100, 120, 150, 160, 200, 240, 300, 400, 480, 600, 800, 1200 and 2400 are the factors of 2400.
Note:
- 2400 is not the perfect square.
- Factors of 2400: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 75, 80, 96, 100, 120, 150, 160, 200, 240, 300, 400, 480, 600, 800, 1200 and 2400
- Prime factors of 2400: 2, 3, 5
Conclusion:
- 2400 is the composite number which has factors 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 75, 80, 96, 100, 120, 150, 160, 200, 240, 300, 400, 480, 600, 800, 1200 and 2400
- And hence, 2400 is not the prime number.
Multiple Choice Questions:
1) 2400 is a
a) Even number
b) Odd number
c) Composite number
d) Both a and c
Ans: d) both a and d
2) The prime factors of a composite number 2400 are
a) 2400
b) 2, 3, 5
c) 1, 4, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 75, 80, 96, 100, 120, 150, 160, 200, 240, 300, 400, 480, 600, 800, 1200 and 2400
d) 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 75, 80, 96, 100, 120, 150, 160, 200, 240, 300, 400, 480, 600, 800, 1200 and 2400
Ans: b) 2, 3, 5
3) 2400 is composite number because
a) It has factors 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 75, 80, 96, 100, 120, 150, 160, 200, 240, 300, 400, 480, 600, 800, 1200 and 2400
b) It has more than two factors
c) Divisible by 2
d) Both a and b
Ans: d) both a and b