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What Are The Prime Factors Of 34

What are the prime factors of 34? Answer: 2, 17

The number 34 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 34 is 17. The smallest prime factor of 34 is 2.

What Is The Factor Tree Of 34

How to use a factor tree to find the prime factors of 34? 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.
    34
    ↙ ↘
    2 × 17

We found 2 prime factors(2, 17) using the factor tree of 34. 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 34 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 34 Are Correct Answers

To know if we got the correct prime factors of 34 we have to get the prime factorization of 34 which is 2 * 17. Because when you multiply the primes of the prime factorization the answer has to be equal with 34.

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

General Mathematical Properties Of Number 34

34 is a composite number. 34 is a composite number, because it has more divisors than 1 and itself. This is an even number. 34 is an even number, because it can be divided by 2 without leaving a comma spot. This also means that 34 is not an odd number. When we simplify Sin 34 degrees we get the value of sin(34)=0.52908268612002. Simplify Cos 34 degrees. The value of cos(34)=-0.84857027478461. Simplify Tan 34 degrees. Value of tan(34)=-0.62349896271623. When converting 34 in binary you get 100010. Converting decimal 34 in hexadecimal is 22. The square root of 34=5.8309518948453. The cube root of 34=3.2396118012775. Square root of √34 simplified is 34. All radicals are now simplified and in their simplest form. Cube root of ∛34 simplified is 34. The simplified radicand no longer has any more cubed factors.

Determine Prime Factors Of Numbers Smaller Than 34

Learn how to calculate primes of smaller numbers like:

Determine Prime Factors Of Numbers Bigger Than 34

Learn how to calculate primes of bigger numbers such as:

Single Digit Properties For Number 34 Explained

  • Integer 3 properties: 3 is odd and a perfect total. The second in the primes sequence, after 2 and before 5, the first to also be Euclidean (3=2+1). One of the primes of Mersenne(3=2²-1), Fermat and Sophie Germain. Three is a component of Ulam, Wedderburn-Etherington, Perrin, Wagstaff. It is integer-free and a triangular number. The fourth issue of the Fibonacci sequence, after 2 and before 5. Belonging to the first Pythagorean terna (3,4,5). The third value of the succession of Lucas, after 1 and before 4. In the numerical decimal system 3 is a Colombian figure. In the binary system they call it a palindrome.
  • Integer 4 properties: 4 is even and the square of 2. Being a composite it has the following divisors:1, 2, 4. Since the sum of the divisors(excluding itself) is 3<4, it is a defective digit. A highly composed, highly totter and highly cototent integer. In mathematic terms four is a component of Ulam, tetrahedral and a part of the Tetranacci Succession. The complete Harshad, which is a number of Harshad in any expressed base. A strictly non-palindrome. The third term of the succession of Mian-Chowla. In the numerical decimal system it is a Smith numeral. A figure is divisible by 4 if and only if its last two digits express a number divisible by four. Each natural value is the sum of at most 4 squares. 4 belongs to the first Pythagorean terna(3,4,5). The fourth issue of the succession of Lucas, after 3 and before 7. Four is a palindrome and a repeated digit in the 3-based positional numbering system.

Finding All Prime Factors Of A Number

We found that 34 has 2 primes. The prime factors of 34 are 2, 17. 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

Knowing these divisibility rules will help you find 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).
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