JUMP TO TOPIC
Factors of 350: Prime Factorization, Methods, and Examples
The factors of 350 are the numbers that give a remainder equal to zero and a whole number as a quotient.
The number 350 is again achieved if we multiply the quotient and the divisor which means that both the quotient and the remainder are the factors of the number 350.
Factors of 350
Here are the factors of number 350.
Factors of 350: 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175 and 350.
Negative Factors of 350
The negative factors of 350 are similar to its positive aspects, just with a negative sign.
Negative Factors of 350: -1, -2, -5, -7, -10, -14, -25, -35, -50, -70, -175 and -350
Prime Factorization of 350
The prime factorization of 350 is the way of expressing its prime factors in the product form.
Prime Factorization: 2 x 5 x 5 x 7
In this article, we will learn about the factors of 350 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.
What Are the Factors of 350?
The factors of 350 are 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175 and 350. These numbers are the factors as they do not leave any remainder when divided by 350.
The factors of 350 are classified as prime numbers and composite numbers. The prime factors of the number 350 can be determined using the prime factorization technique.
How To Find the Factors of 350?
You can find the factors of 350 by 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 350, create a list containing the numbers that are exactly divisible by 350 with zero remainders. One important thing to note is that 1 and 350 are the 350’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 350 are determined as follows:
\[\dfrac{350}{1} = 350\]
\[\dfrac{350}{2} = 175\]
\[\dfrac{350}{5} = 70\]
\[\dfrac{350}{10} = 50\]
\[\dfrac{350}{14} = 25\]
\[\dfrac{350}{350} = 1\]
Therefore, 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175 and 350. are the factors of 350.
Total Number of Factors of 350
For 350, there are 12 positive factors and 12 negative ones. So in total, there are 24 factors of 350.
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 350 is given as:
Factorization of 350 is 1 x 2 x 5$^2$ x 7.
The exponent of 2, and 7 is 1 whereas the exponent of 5 is 2.
Adding 1 to each and multiplying them together results in 24.
Therefore, the total number of factors of 350 is 24. 12 are positive, and 12 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 350 by Prime Factorization
The number 350 is a composite number. 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 350 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 350, 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 350 can be expressed as:
350 = 2 x 5$^2$ x 7
Factors of 350 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 350, the factor pairs can be found as:
1 x 350 = 350
2 x 175 = 350
5 x 70 = 350
7 x 50 = 350
10 x 35 = 350
14 x 25 = 350
The possible factor pairs of 350 are given as (1, 350) ,(2, 175 ),(5 x 70),
(7 x 50),(10 x 35) and (14 x 25).
All these numbers in pairs, when multiplied, give 350 as the product.
The negative factor pairs of 350 are given as:
-1 x -350 = 350
-2 x -175 = 350
-5 x -70 = 350
-7 x -50 = 350
-10 x -35 = 350
-14 x -25 = 350
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, -5, -7, -10, -14, -25, -35, -50, -70, -175 and -350 are called negative factors of 350.
The list of all the factors of 350, including positive as well as negative numbers, is given below.
Factor list of 350: 1, -1, 2, -2, 5, -5, 7, -7, 10, -10, 14, -14, 25, -25, 35, -35, 50, -50, 70, -70, 175, -175, 350 and -350.
Factors of 350 Solved Examples
To better understand the concept of factors, let’s solve some examples.
Example 1
How many factors of 350 are there?
Solution
The total number of Factors of 350 is 12.
Factors of 350 are 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175 and 350..
Example 2
Find the factors of 350 using prime factorization.
Solution
The prime factorization of 350 is given as:
350 $\div$ 2 = 175
175 $\div$ 5 = 35
35 $\div$ 5 = 7
7 $\div$ 7 = 1
So the prime factorization of 350 can be written as:
2 x 5 x 5 x 7 = 350