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# What Are The Prime Factors Of 65

What are the prime factors of 65? Answer: 5, 13

The number 65 has 2 prime factors. Primes can only have two factors(1 and itself) and only be divisible by those two factors. Any figure where this rule applies can be called a prime factor. The biggest prime factor of 65 is 13. The smallest prime factor of 65 is 5.

## What Is The Factor Tree Of 65

How to use a factor tree to find the prime factors of 65? A factor tree is a diagram that organizes the factoring process.

• First step is to find two numbers that when multiplied together equal the number we start with.
65
↙ ↘
5 × 13

We found 2 prime factors(5, 13) using the factor tree of 65. Now let us explain the process to solving factor trees in more detail. Our goal is to find all prime factors of a given whole number. In each step of our factor tree diagram for 65 we always checked both multiplication numbers if they were primes or not. If one or both of the integers are not prime numbers then this means that we will have to make diagrams for them too. This process continues until only prime numbers are left.

Remember that often a factor tree for the same integer can be solved in more than one correct way! An example of this is the figure 12 where 2*6=12 and 4*3=12. The primes of a factor tree for 12 are the same regardles if we start the factor tree with 2*6 or 4*3.

## How To Verify If Prime Factors Of 65 Are Correct Answers

To know if we got the correct prime factors of 65 we have to get the prime factorization of 65 which is 5 * 13. Because when you multiply the primes of the prime factorization the answer has to be equal with 65.

After having checked the prime factorization we can now safely say that we got all prime factors.

## General Mathematical Properties Of Number 65

65 is a composite number. 65 is a composite number, because it has more divisors than 1 and itself. It is not even. 65 is not an even number, because it can't be divided by 2 without leaving a comma spot. This also means that 65 is an odd number. When we simplify Sin 65 degrees we get the value of sin(65)=0.8268286794901. Simplify Cos 65 degrees. The value of cos(65)=-0.56245385123817. Simplify Tan 65 degrees. Value of tan(65)=-1.4700382576632. When converting 65 in binary you get 1000001. Converting decimal 65 in hexadecimal is 41. The square root of 65=8.0622577482985. The cube root of 65=4.0207257585891. Square root of √65 simplified is 65. All radicals are now simplified and in their simplest form. Cube root of ∛65 simplified is 65. The simplified radicand no longer has any more cubed factors.

## Determine Prime Factors Of Numbers Smaller Than 65

Learn how to calculate primes of smaller numbers like:

## Determine Prime Factors Of Numbers Bigger Than 65

Learn how to calculate primes of bigger numbers such as:

## Single Digit Properties For Number 65 Explained

• Integer 6 properties: 6 is even and a composite, with the following divisors:1, 2, 3, 6. Also called perfect number since the sum of the divisors(excluding itself) is 6. The first perfect figure, the next ones are 28 and 496. Six is highly a composed, semiprimo, congruent, scarcely total, Ulam, Wedderburn-Etherington, multi-perfect, integer-free number. Complete Harshad, which is a quantity of Harshad in any expressed base. The factorial of 3 and a semi-perfect digit. The third triangular and the first hexagonal value. All perfect even amounts are triangular and hexagonal. Six is the smallest amount different from 1 whose square (36) is triangular(the next in the line that enjoys this property is 35). Strictly a non-palindrome. A numeral is divisible by 6 if and only if it is divisible by both 2 and 3. Part of the Pythagorean triple (6, 8, 10). Being the product of the first two primes (6=2×3), it is a primitive. In the positional numbering system based on 5 it is a repeated number. An oblong, of the form n(n+1).
• Integer 5 properties: 5 is the third the primes, after 3 and before 7. An odd amount and part of the primes of Fermat, Sophie Germain and Eisenstein. It is a prime, which is (5-1)÷2 and still remains one. Five is a pentagonal, square pyramidal, centered square, pentatopic, Perrin, Catalan and a congruent number. The fifth of the Fibonacci sequence, after 3 and before 8. An untouchable amount, not being the sum of the divisors proper to any other. Figures are divisible by 5 if and only if its last digit is 0 or 5. The square of a quantity with the last digit of 5 is equal to a quantity that has the last digits of 25 and as first digits the product of the private starting of 5 for itself increased by one unit. For example, 25²=(2×3)25=625 or 125²=(12×13)25=15625. The total of the first 2 prime numbers(in fact 2+3=5) and the sum of two squares(5=1²+2²). Five is the smallest natural that belongs to 2 Pythagorean triads:(3, 4, 5) and (5, 12, 13). In the binary system a palindrome. In the positional numbering system based on 4 it is a repeated number. In the numerical decimal system a Colombian number, that in addition is integer-free.

## Finding All Prime Factors Of A Number

We found that 65 has 2 primes. The prime factors of 65 are 5, 13. We arrived to this answer by using the factor tree. However we could have also used upside down division to get the factorization primes. There are more that one method to factorize a integer.

## List of divisibility rules for finding prime factors faster

Rule 1: If the last digit of a figure is 0, 2, 4, 6 or 8 then it is an even number. All even numbers are divisible by 2.

Rule 2: If the sum of digits of a integer is divisible by 3 then the figure is also divisible by 3 and 3 is a prime factor(example: the digits of 12 are 1 and 2 so 1+2=3 and 3 is divisible by 3, meaning that 12 is divisible by 3). The same logic also works for 9.

Rule 3: If the last two digits of a number are 00 then this integer is divisible by 4(example: we know that 124=100+24 and 100 has two zeros in the end making it divisible with 4. We also know that 4 is divisible with 24). In order to use this rule to it's fullest it is best to know multiples of 4.

Rule 4: If the last digit of a number is 0 or 5 then 5 it is divisible by 5.

Rule 5: All integers that are divisible by both 2 and 3 are also divisible by 6. This is logical because 2*3=6.

## What Are Prime Factors Of A Number?

All numbers that are only divisible by one and itself are called prime factors in mathematics. A prime factor is a figure that has only two factors(one and itself).