The factors of 280 are the numbers that never leave a remainder when divided by 280. The number 280 is an even composite number with 16 factors in total.
The factors of numbers can be written with a negative sign and are termed negative factors of the number.
Factors of 280
Here are the factors of number280.
Factors of 280: 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 280
Negative Factors of 280
The negative factors of 280are similar to its positive aspects, just with a negative sign.
Negative Factors of 280: –1, -2, -4, -5, -7, -8, -10, -14, -20, -28, -35, -40, -56, -70, -140, -280
Prime Factorization of 280
The prime factorization of 280is the way of expressing its prime factors in the product form.
Prime Factorization: 2 x 2 x 2 x 5 x 7
In this article, we will learn about the factors of 280and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.
What Are the Factors of 280?
The factors of 280 are1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, and 280. These numbers are the factors as they do not leave any remainder when divided by 280.
The factors of 280are classified as prime numbers and composite numbers. The prime factors of the number 280 can be determined using the prime factorization technique.
How To Find the Factors of 280?
You can find the factors of 280by using the rules of divisibility. The divisibility rule states that any number, when divided by any other natural number, is said to be divisible by the number if the quotient is the whole number and the resulting remainder is zero.
To find the factors of 280, create a list containing the numbers that are exactly divisible by 280 with zero remainders. One important thing to note is that 1 and 280 are the 280’s factors, as every natural number has 1 and the number itself as its factor.
1 is also called the universal factor of every number. The factors of 280 are determined as follows:
\[\dfrac{280}{1} = 280\]
\[\dfrac{280}{2} = 140\]
\[\dfrac{280}{4} = 70\]
\[\dfrac{280}{5} = 56\]
\[\dfrac{280}{7} = 40\]
\[\dfrac{280}{8} = 35\]
\[\dfrac{280}{10} = 28\]
\[\dfrac{280}{14} = 20\]
\[\dfrac{280}{280} = 1\]
Therefore,1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, and 280are the factors of 280.
Total Number of Factors of 280
For 280, there are sixteenpositive factors and sixteennegative ones. So in total, there are thirty-two factors of 280.
To find the total number of factors of the given number, follow the procedure mentioned below:
- Find the factorization/prime factorization of the given number.
- Demonstrate the prime factorization of the number in the form of exponent form.
- Add 1 to each of the exponents of the prime factor.
- Now, multiply the resulting exponents together. This obtained product is equivalent to the total number of factors of the given number.
By following this procedure, the total number of factors of X is given as:
Factorization of 280 is1 x 2$^3$ x 5 x 7.
The exponent of 1, 2, and 5 is 1, whereas the exponent of 2 is 3.
Adding 1 to each and multiplying them together results in 32.
Therefore, the total number of factors of 280 is 32. 16 factors are positive, and 16 factors are negative.
Important Notes
Here are some essential points that must be considered while finding the factors of any given number:
- The factor of any given number must be a whole number.
- The factors of the number cannot be in the form of decimals or fractions.
- Factors can be positive as well as negative.
- Negative factors are the additive inverse of the positive factors of a given number.
- The factor of a number cannot be greater than that number.
- Every even number has 2 as its prime factor, the smallest prime factor.
Factors of 280 by Prime Factorization
The number 280is a composite. Prime factorization is a valuable technique for finding the number’s prime factors and expressing the number as the product of its prime factors.
Before finding the factors of 280 using prime factorization, let us find out what prime factors are. Prime factors are the factors of any given number that are only divisible by 1 and themselves.
To start the prime factorization of 280, start dividing by its most minor prime factor. First, determine that the given number is either even or odd. If it is an even number, then 2 will be the smallest prime factor.
Continue splitting the quotient obtained until 1 is received as the quotient. The prime factorization of 280can be expressed as:
280 = 2 x 2 x 2 x 5 x 7
Factors of 280 in Pairs
The factor pairs are the duplet of numbers that, when multiplied together, result in the factorized number. Factor pairs can be more than one depending on the total number of factors given.
For 280, the factor pairs can be found as:
1 x 280 = 280
2 x 140 = 280
4 x 70 = 280
5 x 56 = 280
7 x 40 = 280
8 x 35 = 280
10 x 28 = 280
14 x 20 = 280
The possible factor pairs of 280are given as(1, 280), (2, 140), (4, 70), (5, 56), (7, 40), (8, 35), (10, 28)and (14, 20).
All these numbers in pairs, when multiplied, give 280 as the product.
The negative factor pairs of 280 are given as:
-1 x -280 = 280
-2 x -140 = 280
-4 x -70 = 280
-5 x -56 = 280
-7 x -40 = 280
-8 x -35 = 280
-10 x -28 = 280
-14 x -20 = 280
It is important to note that in negative factor pairs, the minus sign has been multiplied by the minus sign, due to which the resulting product is the original positive number. Therefore, –1, -2, -4, -5, -7, -8, -10, -14, -20, -28, -35, -40, -56, -70, -140, and -280are called negative factors of 280.
Factors of 280 Solved Examples
To better understand the concept of factors, let’s solve some examples.
Example 1
How many factors of 280 are there?
Solution
The total number of Factors of 280 is 16.
Factors of 280 are1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, and 280.
Example 2
Find the factors of 280 using prime factorization.
Solution
The prime factorization of 280 is given as:
280 $\div$ 2 = 140
140 $\div$ 2 = 70
70 $\div$ 2 = 35
35 $\div$ 5 = 7
7 $\div$ 7 = 1
So the prime factorization of 280 can be written as:
2 x 2 x 2 x 5 x 7 = 280
