Is 750 a prime number?
It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 750, the answer is: No, 750 is not a prime number.
The list of all positive divisors (i.e., the list of all integers that divide 750) is as follows: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 125, 150, 250, 375, 750.
For 750 to be a prime number, it would have been required that 750 has only two divisors, i.e., itself and 1.
Find out more:
Actually, one can immediately see that 750 cannot be prime, because 5 is one of its divisors: indeed, a number ending with 0 or 5 has necessarily 5 among its divisors. The last digit of 750 is 0, so it is divisible by 5 and is therefore not prime.
As a consequence:
- 750 is a multiple of 1
- 750 is a multiple of 2
- 750 is a multiple of 3
- 750 is a multiple of 5
- 750 is a multiple of 6
- 750 is a multiple of 10
- 750 is a multiple of 15
- 750 is a multiple of 25
- 750 is a multiple of 30
- 750 is a multiple of 50
- 750 is a multiple of 75
- 750 is a multiple of 125
- 750 is a multiple of 150
- 750 is a multiple of 250
- 750 is a multiple of 375
For 750 to be a prime number, it would have been required that 750 has only two divisors, i.e., itself and 1.
Is 750 a deficient number?
No, 750 is not a deficient number: to be deficient, 750 should have been such that 750 is larger than the sum of its proper divisors, i.e., the divisors of 750 without 750 itself (that is 1 + 2 + 3 + 5 + 6 + 10 + 15 + 25 + 30 + 50 + 75 + 125 + 150 + 250 + 375 = 1 122).
In fact, 750 is an abundant number; 750 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 5 + 6 + 10 + 15 + 25 + 30 + 50 + 75 + 125 + 150 + 250 + 375 = 1 122). The smallest abundant number is 12.
