If a number completely divides 57 with the remainder zero, then that number is called a factor of 57.
Thus, we can say that the factors of 57 are the divisors of 57. In this section, we will learn about the factors of 57 and the prime factors of 57.
For more details: Basic concepts of factors
Table of Contents
Highlights of Factors of 57
- 57=3×19 is the prime factorization of 57.
- The factors of 57 are 1, 3, 19, and 57.
- Prime factors of 57 are 3 and 19.
- Negative factors of 57 are –1, -3, -19, and –57.
What are the Factors of 57?
Let us write the number 57 multiplicatively in all possible ways. We have:
| 57 = 1×57 |
| 57 = 3×19 |
As we cannot express 57 multiplicatively in any other way, so we will stop right now. So the factors of 57 in pairs are given as follows:
| 57 = a×b | Factors in Pairs (a,b) |
| 57 = 1×57 | (1, 57) |
| 57 = 3×19 | (3, 19) |
Thus the pair factors of 57 are (1, 57) and (3, 19). As all the numbers appearing in pair factors are the factors of 57, we conclude that
|
The factors of 57 are: 1, 3, 19, and 57. |
Number of Factors of 57
From above we have calculated the factors of 57 which are 1, 3, 19, and 57. Thus the total number of factors of 57 is four.
Prime Factors of 57
Note that the factors of 57 are 1, 3, 19, and 57. Among those factors, we notice that only 3 and 19 are prime numbers as they do not have any proper divisors.
∴ The prime factors of 57 are 3 and 19.
Question: What are the factors of 57?
Video Solution: coming soon…
How to Find Factors of 57?
Now we will determine the factors of 57 by division method. In this method, we will find the numbers that can divide 57 with no remainder. See that
57÷1=57 and the remainder is 0.
∴ 1 and 57 are factors of 57.
57÷3=19 and the remainder is 0.
∴ 3 and 19 are factors of 57.
Note that no numbers other than the numbers in violet color can divide 57. So the numbers in violet color, that is, 1, 3, 19, and 57 are the complete list of factors of 57.
