How to Find the Factors of 318 Step by Step
Factor of a number is an integer that divides the given number evenly. A prime number has at least 4 (including negative factors) factors. A composite number has more than 4 factors. Now, coming to the main topic of our article, What are factors of 318? The answer is, a factor of 318 divides 318 evenly. If a number has multiple which is equal to 318 then the number is a factor of 318.
To answer our question, What are factors of 318? we need to discuss the factor of 318, what we truly mean is all the positive and negative whole numbers that can divide 318. The result of taking the number 318 and dividing it by one of its factors would be another factor of it.
Let's examine how to identify and list each of the 318 elements.
These numbers can be written as individual factors or factor pairs and can divide 318 into equal parts. We present them both ways. This is a specific number's mathematical decomposition.
How to Find the Factors of 318
The factor of 318 can be calculated by finding all divisors of 318 that divide completely. Since 318 is an even number, it is divisible by 2 and 2 is the least prime number.
\[318 \div 2 = 159\]
Thus 2 is a factor of 318.
Now find the least prime factor that divides quotients evenly.
159 is an odd number, thus it is not divisible by 2.
The sum of the digits is 1+5+9 = 15 which is divisible by 3.
Thus 159 is divisible by 3.
\[159 \div 3 =53\]
Thus 3 is a factor of 318.
Now 53 is a prime number, it is only divisible by 53.
\[53\div 53=1\]
Thus 53 is a factor of 318.
The product of any two factors is also a factor of 318.
Thus \[2 \times 3 = 6, 2\times 53 = 106, 3 \times 53 = 159\] are also a factor of 318.
A number is divisible by 1 and 318, thus 1 and 318 are factors of 318.
The factors of 318 are 1,2,3,6,53,106,159, and 318.
Negative Factors:
A negative integer can divide a positive number, but the quotient will be a negative number.
\[318 \div (-1) = -318\]
\[318 \div (-2) = -159\]
\[318 \div (-3) = -106\]
\[318 \div (-6) = -53\]
\[318 \div (-53) = -6\]
\[318 \div (-106) = -3\]
\[318 \div (-159) = -2\]
\[318 \div (-318) = -1\]
Thus -1,-2,-3,-6,-53,-106,-159, and -318 divides 318 evenly. Thus -1, -2, -3, -6, -53, -106, -159, and -318 are the factors of 318.
Prime Factorization:
Prime factorization of a number is a process to find prime factors of a number. To find factors of 318 by prime factorization, First we will divide 318 by the least prime that divides 318 evenly. In the same manner we divide quotients by least prime.
The product of prime numbers is 318. The prime factors of 318 by prime factorisation are 2,3,53.
Factor Tree of 318
Tree diagram is a pictorial representation of prime factorization of a number. It shows all prime factors of 318.
Factor tree of 318
Factor of 318 in Pairs
Factor pair looks like an ordered pair consisting of two elements. The number of factor pairs of numbers is equal to the half number of factors of a number. To find factor pairs, we will arrange the factors ascending and descending order. For the first factor pair:the first element will be the first number of ascending order and the second element will be the first element of descending order. For the second factor pair: the first element will be the second number of ascending order and the second element will be the second element of descending order. In the same manner we will find rest of them
Ascending order: 1,2,3,6,53,106,159,318
Descending order:318,159,106,53,6,3,2,1
Then the factors of 318 in pairs are (1, 318), (2, 159), (3, 106), (6, 53), (53, 6), (105, 3), (159, 2), (318, 1).
For negative factors
Ascending order:-318,-159,-106,-53,-6,-3,-2,-1
Descending order:-1,-2,-3,-6,-53,-106,-159,-318
(-318,-1),(-159,-2),(-105,-3),(-53,-6),(-6,-53),(-3,-106),(-2,-159),(-1,-318).
Order pairs are commutative. This means (a,b) = (b,a).
The order pairs are(1,318),(2,159),(3,106),(6,53), (-318,-1),(-159,-2),(-105,-3)and (-53,-6).
Number of Positive Factors:
The number of factors of a number depends on the exponent of prime factors of the given number. Assume N is a composite number and X, Y, and Z are prime factors of N such that \[N = X^aY^bZ^c\].
The formula of the number of positive factors of N is (a+1)(b+1)(c+1).
The prime factorization of 318 is \[2\times 3\times 53\].
Thus the number of positive factors of 318 is (1+1)(1+1)(1+1) = 8.
Sum of Factors:
The factors of 318 are 1,2,3,6,53,106,159,318,-1,-2,-3,-6,-53,-106,-159,-318.
Thus the sum of factors is 1+2+3+6+53+106+159+318+(-1)+(-2)+(-3)+(-6)+(-53)+(-106)+(-159)+(-318) =0
Solved Examples
Example 1: What is the sum of non prime factors of 318?
Sol: The prime factorization of 318 is
The prime factor of 318 is 2,3,53. The products of any two prime factors are \[2 \times 3 = 6, 2 \times 53 = 106, 3 \times 53 = 159\]. The negative value of the factors is also a factor of the number.
The factors of 318 are 1,2,3,6,53,106,159, 318,-1,-2,-3,-6,-53,-106,-159, -318.
The non prime factors are 6,106,159, 318,-1,-2,-3,-6,-53,-106,-159, -318.
The sum of the non prime factors are
6+106+159+318+(-1)+(-2)+(-3)+(-6)+(-53)+(-106)+(-159)+( -318) = -59.
Example 2: What is the sum of prime factors of 318?
Sol: The prime factorization of 318 is
The prime factor of 318 is 2,3,53. The sum of the prime factors is 2+3+53 = 59
Example 3: What is the highest factor of 318?
Sol: The prime factorization of 318 is
The prime factor of 318 is 2,3,53. The products of any two prime factors are \[2 \times 3 = 6, 2 \times 53 = 106, 3 \times 53 = 159\]. The negative value of the factors is also a factor of the number.
The factors of 318 are 1,2,3,6,53,106,159, 318,-1,-2,-3,-6,-53,-106,-159, -318.
The highest factor of 318 is 318.
Key Features about Number 318 and its Factors
318 is a composite number rather than a prime number.
The composite number 318 has the following prime factors:
\[318 = 2 \times 3 \times 53\]The factors 318, 159, 106, 53, 6, 3, 2, 1 and all the negatives -318, -159, -106, -53, -6, -3, -2, -1 all of these can exactly divide 318.
Conclusion
The factors of 318 are 318, 159, 106, 53, 6, 3, 2, 1,-318, -159, -106, -53, -6, -3, -2, -1. The prime factors of 318 are 2,3,53. As the number of positive factors is 8. Since the number of factors of 318 is more than 2, then 318 is a composite number.
List of Related Articles
Practice on Your Own
Q 1: What is the product of the two highest factors of 318?
Ans: 50562.
Q 2: What are the common factors in 318 and 87?
Ans: 1 and 3.
FAQs on Factors of 318 Explained with Prime Factorization
1. What are the factors of 318?
The factors of 318 are 1, 2, 3, 6, 53, 106, 159, and 318. These are the positive integers that divide 318 exactly without leaving a remainder.
- 318 ÷ 1 = 318
- 318 ÷ 2 = 159
- 318 ÷ 3 = 106
- 318 ÷ 6 = 53
2. How do you find the factors of 318?
To find the factors of 318, divide 318 by integers starting from 1 up to its square root. Follow these steps:
- Check divisibility by 1, 2, 3, and so on.
- Stop at √318 (approximately 17.8).
- List both the divisor and quotient when division is exact.
3. What is the prime factorization of 318?
The prime factorization of 318 is 2 × 3 × 53. Breaking it down step-by-step:
- 318 ÷ 2 = 159
- 159 ÷ 3 = 53
- 53 is a prime number
4. How many factors does 318 have?
The number 318 has 8 positive factors. Using the prime factorization 318 = 2¹ × 3¹ × 53¹, apply the formula for total factors:
- Add 1 to each exponent: (1+1)(1+1)(1+1)
- Multiply: 2 × 2 × 2 = 8
5. What are the factor pairs of 318?
The factor pairs of 318 are (1, 318), (2, 159), (3, 106), and (6, 53). Each pair multiplies to give 318. For example:
- 2 × 159 = 318
- 6 × 53 = 318
6. Is 318 a prime or composite number?
The number 318 is a composite number because it has more than two factors. A prime number has exactly two factors (1 and itself), but 318 has 8 factors: 1, 2, 3, 6, 53, 106, 159, and 318. Therefore, 318 is composite.
7. What is the greatest common factor (GCF) of 318 and 159?
The greatest common factor (GCF) of 318 and 159 is 159. Since 318 ÷ 159 = 2 exactly, 159 divides both numbers. Therefore, 159 is the largest number that is a factor of both 318 and 159.
8. What is the sum of all factors of 318?
The sum of all positive factors of 318 is 648. Add all the factors:
- 1 + 2 + 3 + 6 + 53 + 106 + 159 + 318
9. What are the multiples of 318?
The multiples of 318 are numbers obtained by multiplying 318 by whole numbers. The first few multiples are:
- 318 × 1 = 318
- 318 × 2 = 636
- 318 × 3 = 954
- 318 × 4 = 1272
10. What is the smallest and greatest factor of 318?
The smallest factor of 318 is 1 and the greatest factor is 318. Every positive integer has 1 as its smallest factor and the number itself as its greatest factor. This rule applies to 318 as well.
