Factors
Factors of 86 | Prime Factorization of 86 | Factor Tree of 86
Written by Prerit Jain
Updated on: 12 Jun 2023
Contents
Factors of 86 | Prime Factorization of 86 | Factor Tree of 86
Factors of 86
| Factors of 86 | Factor Pairs of 86 | Prime factors of 86 |
| 1, 2, 43, 86 | (1,86) (2,43) (43,2) | 2 x 43 |
Calculate Factors of
The Factors are
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What are the factors of 86
The factors of 86 are the numbers that can divide into 86 without leaving a remainder. In other words, the factors of 86 are the numbers that can evenly divide into 86.
Here is a list of the factors of 86:
1, 2, 43, and 86
To find the factors of 86, we can list out all the numbers that can be multiplied together to get 86:
1 x 86 = 86
2 x 43 = 86
We can also find the factors of 86 by using the prime factorization of 86, which is 2 x 43. The factors of 86 include all the combinations of these prime numbers.
How to Find Factors of 86
There are several ways to find the factors of 86:
- Factors of 86 using the Multiplication Method
- Factors of 86 using the Division Method
- Prime Factorization of 86
- Factor tree of 86
Factors of 86 Using the Multiplication Method
The multiplication method for finding the factors of a number involves listing out all the pairs of numbers that can be multiplied together to get the original number.
To find the factors of 86 using the multiplication method, we can list out all the pairs of numbers that can be multiplied together to get 86:
1 x 86 = 86
2 x 43 = 86
The factors of 86 using the multiplication method are 1, 2, 43, and 86.
Factors of 86 Using the Division Method
To find the factors of 86 using the division method, we can start by dividing 86 by the smallest possible factor and then continue dividing the result by the smallest possible factor until we can’t divide anymore.
Here is the process for finding the factors of 86 using the division method:
- Begin by dividing 86 by the smallest possible factor, which is 1. If the result is a whole number, then 1 is a factor of 86.
- Divide the result by the next smallest factor. If the result is a whole number, then that factor is also a factor of 86.
- Continue dividing the result by the next smallest factor until we can’t divide anymore.
Using this method, we can find all the factors of 86.
Prime Factorization of 86
Calculate Prime Factors of
The Prime Factors of 86 =
2 x
43
The prime factorization of 86 is the expression of 86 as the product of its prime factors. To find the prime factorization of 86, we can follow these steps:
- Find the smallest prime number that divides into 86. In this case, the smallest prime number is 2.
- Divide 86 by 2. The result is 43.
- Check if 43 is a prime number. If it is, then the prime factorization of 86 is 2 x 43. If it is not, then we need to continue the process.
- Find the smallest prime number that divides into 43. In this case, the smallest prime number is 3.
- Divide 43 by 3. The result is 14.
- Check if 14 is a prime number. If it is, then the prime factorization of 86 is 2 x 3 x 14. If it is not, then we need to continue the process.
- Find the smallest prime number that divides into 14. In this case, the smallest prime number is 2.
- Divide 14 by 2. The result is 7.
- Check if 7 is a prime number. If it is, then the prime factorization of 86 is 2 x 3 x 2 x 7 or 2 x 2 x 3 x 7. If it is not, then we need to continue the process.
- Find the smallest prime number that divides into 7. In this case, the smallest prime number is 7.
- Divide 7 by 7. The result is 1.
Factor tree of 86
A factor tree is a graphical representation of the prime factorization of a number. To create a factor tree for 86, we can follow these steps:
- Write the number 86 at the top of a piece of paper.
- Draw a line below 86 and write the smallest prime number that divides into 86 on the left side of the line and the result of the division on the right side of the line.
- Draw a line below the result of the division and write the smallest prime number that divides into it on the left side of the line and the result of the division on the right side of the line.
- Continue this process until we get a result of 1 on the right side of the line.
Factor Pairs of 86
Calculate Pair Factors of
1 x 86=86
2 x 43=86
43 x 2=86
So Pair Factors of 86 are
(1,86)
(2,43)
(43,2)
The factor pairs of a number are the pairs of numbers that multiply together to equal that number. For example, the factor pairs of 86 are the pairs of numbers that multiply together to equal 86.
Some of the factor pairs of 86 are:
- A number and 86. For example, 1 x 86 is a factor pair of 86.
- Two numbers whose product is 86. For example, 2 x 43 is a factor pair of 86.
- Three numbers whose product is 86. For example, 3 x 28 is a factor pair of 86.
More Factors
Factors of 86 – Quick Recap
- Factors of 86: 1, 2, 43, 86.
- Negative Factors of 86: 1, -2, -43, and -86.
- Prime Factors of 86: 2 and 43.
- Prime Factorization of 86: 2 and 43.
Factors of 86 – Fun Facts
- The factors of 86 are the numbers that divide evenly into 86.
- The factors of 86 include all the prime numbers that divide into 86, as well as 1 and 86 itself.
- The factors of 86 also include all the composite numbers that are formed by multiplying together the prime factors of 86.
- The number of factors of 86 is equal to the number of divisors of 86.
- The sum of the factors of 86 is equal to the sum of the divisors of 86.
Also Check: Multiples, Square Root, and LCM
Solved Examples of Factor of 86
Q.1: What is the smallest number that can go into 86?
Solution: The smallest number that can go into 86 is 1 since any number divided by 1 will remain unchanged.
Q.2: Find the prime factorization of 86.
Solution: The prime factorization of 86 is 2 x 43; since 2 x 43 = 86.
Q.3: How many even factors does 86 have?
Solution: There are 5 even factors of 86; 1, 2, 43 and 86.
Q.4: List all the pairs of factors for 86 in increasing order.
Solution: The pairs of factors for 86 in increasing order are (1,86 ), and (2,43).
Q.5: What is the greatest common factor for 81 and 87?
Solution: The greatest common factor for 81 and 87 is 3 since 3 is the only integer between them which can be evenly divided into both numbers without a remainder (no shared divisors) .
Q.6: Is there any perfect square within the range of numerators from 85 to 89?
Solution: None of the numbers in the range have integer square roots. Therefore, there are no perfect squares within the range of numerators from 85 to 89.
Q.7: Does 84 have any cube factors? If so name them…
Solution: Among the prime factors, we have two 2s, one 3, and one 7. None of these prime factors occurs in groups of three. Therefore, 84 does not have any cube factors.
Q.8: What would be the least common multiple between 77 and 83?
Solution: The least common multiple between 77 and 83 is 6391.
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Frequently Asked Questions on Factors of 86
What is the prime factorization of 86?
The prime factorization of 86 is 86 = 2 x 43.
How many factors does 86 have?
There are 6 factors of 86; 1,2,43,86.
Is 86 an abundant number?
No, 86 is not an abundant number because the sum of its divisors (1 + 2 + 3 + 6 + 43) is less than the original number (86).
How many pairs of factors equal to 86 can you find?
There are 2 pairs of factors that equal 86; (1,86), (2,43).
What is the greatest common factor for 84 and 88?
The greatest common factor for 84 and 88 is 4.
What type of number is 86?
The number 86 is a composite number since it has more than two distinct divisors greater than one.
Does 87 have any square factors?
The prime factorization of 87 is 3 * 29.
To have a square factor, a number must have an even exponent for each of its prime factors. In the case of 87, none of its prime factors (3 and 29) have even exponents.
Therefore, 87 does not have any square factors.
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