What are the Factors of 57?
The factors of 57 are natural numbers that divide 57 evenly. In other words, each factor of 57 divides 57 without leaving a remainder.
The factors of 57 are 1, 3, 19 and 57 mainly because all these numbers divide 57 completely.
List of Factors of 57
Divisibility rules and division facts can be used to determine the factors of 57.
We can stop the derivation of factors with this step because the multiplication equations will start to repeat for higher numbers. So, the factors of 57 are the multiplicands of each multiplication equation. Since there are 2 multiplication equations with unique multiplicands, the number 57 has four factors, which are, 1, 3, 19 and 57.
Prime Factorization of 57
Prime factorization implies that we express a number as a product of prime numbers. The prime numbers multiplied here are known as the prime factors of that number.
The factor tree of 57 that is represented as an image describes the prime factorization of 57.
So, the prime factorization of 57 is 57 = 3 x 19.
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Factor Pairs of 57
The factor pair of a number is a set of two factors of that number whose product provides the original number.
The factor pairs of 57 are the pairs of its factors whose product is 57. For example: (3, 19) is a factor pair of 57, since ‘3 x 19 = 57’.
Factor of Pairs 57
Solved Factors of 57 Examples
Example 1: Find the common factors of 26 and 57.
Solution:
Factors of 26: 1, 2, 13 and 26.
Factors of 57: 1, 3, 19 and 57
So, the common factor of 26 and 57 is 1.
Example 2: Find the greatest common factor of 36 and 57.
Solution:
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18 and 36
Factors of 57: 1, 3, 19 and 57
The common factors of 36 and 57 are 1 and 3.
So, the greatest common factor of 36 and 57 is 3.
Example 3: Sam was studying geometrical shapes and found a rectangle of area 57 square centimeters. What are the possible dimensions of the rectangle?
Solution :
The area of rectangle = l x w
Where, l is length, and w is width of rectangle
57 = l x w
The product of width and length is 57.
The possible dimensions of width and length can be listed from the factor pairs of 57:
Yes, 19 divides 57 completely, that is, if we divide 57 by 19 then we get 0 as remainder, and 3 as quotient.
The factors of 57 are 1, 3, 19 and 57.
Sum of factors = 1 + 3 + 19 + 57 = 80.
The factor pairs of 57 are the pair of numbers whose product is 57. The factor pairs of 57 are (1, 57) and (3, 19).
The factors of 57 are 1, 3, 19 and 57. So, its greatest and least factors are 57 and 1 respectively.
The factors of 57 are 1, 3, 19 and 57.
Product of factors of 57 = 1 x 3 x 19 x 57 = 3249.