What times what equals 17?
The Correct Answer and Explanation is :
The two numbers that multiply to equal 17 are 1 and 17.
Explanation:
To understand how multiplication works, it’s important to remember that multiplication is essentially repeated addition. So, when we say “1 times 17,” we are simply adding 17 one time:
[
1 \times 17 = 17
]
Similarly, when we say “17 times 1,” we are adding 17 seventeen times, but since it’s multiplied by 1, it remains 17:
[
17 \times 1 = 17
]
Now, in the case of the number 17, it is a prime number, meaning it only has two positive divisors: 1 and 17. A prime number cannot be divided evenly by any other number except for 1 and itself. So, the only factors of 17 are 1 and 17.
In mathematics, a factor is a number that divides another number exactly without leaving a remainder. Since 17 is a prime, its only factors are 1 and 17. This means that no other number will multiply with another to give 17, except for 1 and 17. In contrast, non-prime numbers, like 12 or 18, have multiple factors—12, for instance, has factors like 1, 2, 3, 4, 6, and 12.
For instance:
[
12 \times 1 = 12
]
[
6 \times 2 = 12
]
[
3 \times 4 = 12
]
But for 17, there is only the pair:
[
1 \times 17 = 17
]
Thus, the only solution to “what times what equals 17?” is 1 and 17. This demonstrates the unique property of prime numbers and how multiplication involving them works.