In Mathematics, factors of 57 are the real numbers that divide the original number in equal number of parts or uniformly. For example, 2 is the factor of 6, because 2 divides 6 into three equal parts. Since 57 is a composite number, it has more than two factors. We can easily find these factors with the help of the division method.
Apart from the factors of 57, we will be evaluating the prime factors that could divide 57 evenly and pair factors that are a pair of two numbers, the product of which results in the original number.
| Factors | Pair Factors | Prime Factors |
| 1, 3, 19, and 57 | (1, 57) and (3, 19) | 57 = 3 x 19 |
How to Find Factors of 57?
Factors of 57 are the real numbers that divide the original number, uniformly. Since 1 is the factor of all the numbers, therefore, it will be a factor of 57 also. Now the other factors could be calculated by division method, keeping in mind the remainder that should be equal to zero.
57 ÷ 1 = 57
57 ÷ 3 = 19
57 ÷ 19 = 3
57 ÷ 57 = 1
Since, all the above four divisions do not generate a fraction but a whole number, and the remainder left for each division is zero, thus, the factors of 57 are 1, 3, 19, and 57.
More Factors |
Pair Factors of 57
Pair factors are also the real numbers that result in the original number (in this case 57) when multiplied in a pair. Since product of 1 and 57 is 57, thus (1, 57) is a pair factor. Hence,
1 × 57 = 57
3 × 19 = 57
No other pair factors can be calculated that could result in 57. Therefore, the pair factors are (1, 57) and (3, 19).
Now, if we consider the negative pair factors, then the product of two negative factors will result in 57.
-1 × -57 = 57
-3 × -19 = 57
Therefore, the negative pair factors are (-1, -57) and (-3, -19).
Prime Factorisation of 57
Prime factors are the prime numbers that can divide the original number, 57, completely. The list of prime numbers between 1 and 57 is given below to figure out the prime factors.
List of prime numbers (1 to 57) :
| 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53 |
Step 1: From the above, it is obvious that 57 is completely divisible by 3. Thus, the smallest prime factor for 57 is 3.
57/3 = 19
Step 2: Now, 19 itself is a prime number, thus it is divisible by either 1 or itself.
19/19 = 1
We cannot divide further, since 1 is a factor of itself.
Therefore,
| Prime factorisation of 57 = 3 x 19 |
Video Lesson on Prime Factors
Solved Examples
Q.1: If 3 bags are bought for Rs.57. Then what is the cost of each bag?
Solution: Given,
Number of bags bought = 3
Cost of 3 bags = Rs. 57
Cost of each bag = 57/3 = 19
Therefore, each bag cost Rs. 19.
Q.2: Find the sum of all the factors of 57.
Solution: The factors of 57 are 1, 3, 19, and 57.
Sum = 1 + 3 + 19 + 57 = 80
Therefore, 80 is the required sum.
Q.3: What is the common factor of 47 and 57?
Answer: Let us write the factors of both the numbers.
57 → 1, 3, 19, 57
47 → 1, 47
Hence, the common factor is only 1.
Q.4: What is the GCF of 57, 27, 81?
Solution: Let us list down the factors of all the given numbers.
27 → 1, 3, 9, 27
57 → 1, 3, 19, 57
81 → 1, 3, 9, 27, 81
Therefore, the greatest common factors of 27, 57 and 81 are 1 and 3.
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Frequently Asked Questions on Factors of 57
What are the factors of 57?
There are a total of four factors of 57. These factors are 1, 3, 19, and 57.
How is 57 represented as the product of prime factors?
The prime factorisation of 57 is:
57 = 3 x 19
What are the multiples of 57?
The first 10 multiples of 57 are 57, 114, 171, 228, 285, 342, 399, 456, 513 and 570.
Is 57 divisible by 7?
No, 57 is not divisible by 7, because after division the remainder is not equal to zero.
57/7 → 8 (Remainder = 1)
Is 57 a prime number or a composite number?
57 is a composite number because it has more than 2 factors.
Is 57 a perfect square?
No, 57 is not a perfect square. Square root of 57 is not a whole number.
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