The number 71 is a prime number, which means that it can only be divided by 1 and itself; it has no other factors. Because of this, the only factor pairs of 71 that are even remotely possible are (1, 71) and (71, 1).

The number 71 can be factorized into its prime factors, which will help us understand why it is a prime. Because 71 is not divisible by any of the smaller prime numbers, its factorization into primes is expressed as 71 multiplied by 1.

Another method for determining whether or not 71 is a prime number is to examine whether or not it can be divided by all of the prime numbers that are less than or equal to the square root of 71. Given that the square root of 71 is close to 8.4, we only need to check whether or not the number can be divided by the prime numbers 2, 3, 5, and 7. The fact that 71 cannot be evenly divided by any of these numbers demonstrates that it is, in fact, a prime number.

Because 71 is a prime number, it is not divisible by any other prime number, so the only numbers that can factor into 71 are 1 and 71 themselves. In conclusion, the only numbers that can factor into 71 are 1 and 71. This comprehension of factors and prime numbers is essential for many applications of mathematics, such as number theory, algebra, and cryptography.