Factors of 250 Using Prime Factorization
What are the Factors of 250?
Integers that divide 250 evenly without leaving any remainder are known as factors of 250. In other words the numbers that are multiplied together in pairs resulting in the number 250 are the factors of 250.
If we divide the number 250 by a number and this results in a nonzero remainder, the number will not be a factor of 250. The factors of 250 can be positive or negative, but cannot be fractions or decimals, as introduced. The factors of 250 are 1, 2, 5, 10, 25, 50, 125 and 250.
Applying Divisibility Rules to Find Factors of 250
We can find the factors of 250 by applying the divisibility rules as well as division facts.
Divisor | Is the number a factor of 250 | Multiplication equation |
|---|---|---|
1 | Yes, 1 is a factor of every number. | 1 \( \times \) 250 = 250 |
2 | Yes, 250 is even. | 2 \( \times \) 125 = 250 |
3 | No, 2 + 5 + 0 = 7 is not divisible by 3. | - |
4 | No, 250 \( \div \) 4 = 62 R2 | - |
5 | Yes, ones digit is 0. | 5 \( \times \) 150 = 250 |
6 | No, 250 is even but not divisible by 3. | - |
7 | No, 250 \( \div \) 7 = 35 R5 | - |
8 | No, 250 \( \div \) 8 = 31 R2 | - |
9 | No, 250 \( \div \) 9 = 27 R7 | - |
10 | Yes, ones digit is 0. | 10 \( \times \) 25 = 250 |
Prime Factorization of 250
The process of writing 250 as a multiplication of prime numbers is known as prime factorization.
The prime factorization of 250 can be represented using a factor tree as follows:
So, the prime factorization of 250 is 250 = 2 \( \times \) 5 \( \times \) 5 \( \times \) 5 or 2 \( \times \) 5\( ^3 \) .
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Factor Pairs of 250
The factor pairs of a number are a set of two factors of the number, such that their product is the number itself.
Positive factor of 92 | Positive factor pair of 92 |
|---|---|
1 \( \times \) 250 | (1, 250) |
2 \( \times \) 125 | (2, 125) |
5 \( \times \) 50 | (5, 50) |
10 \( \times \) 25 | (10, 250) |
We can also write the factor pairs in ordered pairs:(1, 250), (2, 125), (5, 50), (10, 25)
Solved Factors of 250 Examples
Example 1: Find the common factor of 100 and 250.
Solution:
The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50 and 100.
And the factors of 250 are 1, 2, 5, 10, 25, 50, 125 and 250
Therefore, the common factors of 100 and 250 are 1, 2, 5, 10, 25, and 50.
Example 2: Find the greatest common factor of 200 and 250.
Solution:
The factors of 200 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100 and 200.
The factors of 250 are 1, 2, 5, 10, 25, 50, 125 and 250.
The common factors of 200 and 250 are 1, 2, 5, 10, 25, and 50. Highest number among them is 50.
Therefore, the greatest common factor of 200 and 250 is 50.
Example 3: Find the sum of all the factors of 250.
Solution:
Factors of 250 are 1, 2, 5, 10, 25, 50, 125 and 250.
Sum of factors = 1 + 2 + 5 + 10 + 25 + 50 + 125 + 250
= 372
So, the sum of all the factors of 250 is 372.
Example 4: Alex had a rectangular farm whose area is 250 square yards. What are the possible dimensions for this piece of land? Provide your answers as integers.
Solution :
The area of rectangular land is calculated by multiplying its length and breadth. The possible dimensions are:
Area of a rectangle = length \( \times \) width
Length in yards | Width in yards |
|---|---|
1 | 250 |
2 | 125 |
5 | 50 |
10 | 25 |
25 | 10 |
50 | 5 |
125 | 2 |
250 | 1 |
Composite numbers are numbers that have factors other than 1 or itself. For example 10, 18, 24 are composite numbers.
The factors of 250 are 1, 2, 5, 10, 25, 50, 125 and 250.
So, the smallest factor of 250 is 1 and the greatest factor is 250.
If we divide 250 by 15 then it results in 10 as the remainder. So, 15 is not a factor of 250.
Yes, 250 is a composite number as it has factors other than one and itself. It has factors 2, 5, 10, 25, 50 and 125, in addition to 1 and itself.