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Factors of 734: Prime Factorization, Methods, and Examples
The numbers 2, 367, and 1,734 when multiplied give in result the number 734.
Thus, this shows these two are factor pairs of 734 and the numbers 1,2,367 and 734 are factors of 734.
Factors of 734
Here are the factors of number 734.
Factors of 734: 1, 2, 367, and 734.
Negative Factors of 734
The negative factors of 734 are similar to its positive aspects, just with a negative sign.
Negative Factors of 734: -1, -2, -367, and -734
Prime Factorization of 734
The prime factorization of 734 is the way of expressing its prime factors in the product form.
Prime Factorization: 2 x 367
In this article, we will learn about the factors of 734 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.
What Are the Factors of 734?
The factors of 734 are 1, 2, 367, and 734. These numbers are the factors as they do not leave any remainder when divided by 734.
The factors of 734 are classified as prime numbers and composite numbers. The prime factors of the number 734 can be determined using the prime factorization technique.
How To Find the Factors of 734?
You can find the factors of 734 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 734, create a list containing the numbers that are exactly divisible by 734 with zero remainders. One important thing to note is that 1 and 734 are the 734’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 734 are determined as follows:
\[\dfrac{734}{1} = 734\]
\[\dfrac{734}{2} = 367\]
\[\dfrac{734}{367} = 2\]
\[\dfrac{734}{734} = 1\]
Therefore, 1, 2, 367, and 734 are the factors of 734.
Total Number of Factors of 734
For 734, there are four positive factors and four negative ones. So in total, there are eight factors of 734.
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 734 is given as:
Factorization of 734 is 2 x 367.
The exponent of 2 and 367 is 1,1.
Adding 1 to each and multiplying them together results in 4.
Therefore, the total number of factors of 734 is eight. Four are positive, and four 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 734 by Prime Factorization
The number 734 is 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 734 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 734, 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 734 can be expressed as:
734 = 2 x 367
Factors of 734 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 734, the factor pairs can be found as:
1 x 734 = 734
2 x 367 =734
The possible factor pairs of 734 are given as (1, 734) and (2, 367).
All these numbers in pairs, when multiplied, give 734 as the product.
The negative factor pairs of 734 are given as:
-1 x -734 = 734
-2 x -367 = 734
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, -367, and -734 are called negative factors of 734.
The list of all the factors of 734, including positive as well as negative numbers, is given below.
Factor list of 734: 1, -1, 2, -2, 367, -367, 734, and -734
Factors of 734 Solved Examples
To better understand the concept of factors, let’s solve some examples.
Example 1
How many factors of 734 are there?
Solution
The total number of Factors of 734 is four.
Factors of 734 are 1, 2, 367, and 734.
Example 2
Find the factors of 734 using prime factorization.
Solution
The prime factorization of 734 is given as:
734 $\div$ 367 = 2
2 $\div$ 2 = 1
So the prime factorization of 734 can be written as:
2 x 367 = 734