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What Are The Prime Factors Of 69

What are the prime factors of 69? Answer: 3, 23

The number 69 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 69 is 23. The smallest prime factor of 69 is 3.

What Is The Factor Tree Of 69

How to use a factor tree to find the prime factors of 69? 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.
    69
    ↙ ↘
    3 × 23

We found 2 prime factors(3, 23) using the factor tree of 69. 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 69 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 69 Are Correct Answers

To know if we got the correct prime factors of 69 we have to get the prime factorization of 69 which is 3 * 23. Because when you multiply the primes of the prime factorization the answer has to be equal with 69.

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

General Mathematical Properties Of Number 69

69 is a composite number. 69 is a composite number, because it has more divisors than 1 and itself. It is not even. 69 is not an even number, because it can't be divided by 2 without leaving a comma spot. This also means that 69 is an odd number. When we simplify Sin 69 degrees we get the value of sin(69)=-0.11478481378319. Simplify Cos 69 degrees. The value of cos(69)=0.99339037972227. Simplify Tan 69 degrees. Value of tan(69)=-0.11554854579453. When converting 69 in binary you get 1000101. Converting decimal 69 in hexadecimal is 45. The square root of 69=8.3066238629181. The cube root of 69=4.1015659297023. Square root of √69 simplified is 69. All radicals are now simplified and in their simplest form. Cube root of ∛69 simplified is 69. The simplified radicand no longer has any more cubed factors.

Determine Prime Factors Of Numbers Smaller Than 69

Learn how to calculate primes of smaller numbers like:

Determine Prime Factors Of Numbers Bigger Than 69

Learn how to calculate primes of bigger numbers such as:

Single Digit Properties For Number 69 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 9 properties: 9 is odd and the square of 3. It is a composite, with the following divisors:1, 3, 9. Since the quantity of the divisors(excluding itself) is 4<9, it is a defective number. In mathematics nine is a perfect total, suitable and a Kaprekar figure. Any amount is divisible by 9 if and only if the quantity of its digits is. Being divisible by the count of its divisors, it is refactorizable. Each natural is the sum of at most 9 cubes. If any sum of the digits that compose it is subtracted from any natural, a multiple of 9 is obtained. The first odd square and the last single-digit quantity. In the binary system it is a palindrome. Part of the Pythagorean triples (9, 12, 15), (9, 40, 41). A repeated number in the positional numbering system based on 8. Nine is a Colombian digit in the numerical decimal system. If multiplied 9 always leads back to itself: 2×9=18 → 1+8=9, 3×9=27 → 2+7=9 in the same way if you add a number to 9, the result then refers to the initial digit: 7+9=16 → 1+6=7, 7+9+9=25 → 2+5=7, 7+9+9+9=34 → 3+4=7. If you put 111111111 in the square (ie 1 repeated 9 times) you get the palindrome 12345678987654321, also if you add all the numbers obtained: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 you get 81, and in turn 8 + 1 = 9.

Finding All Prime Factors Of A Number

We found that 69 has 2 primes. The prime factors of 69 are 3, 23. 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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