what is the prime factorization of 65

Factor 65 Factor of 65 are numbers that, when multiplied in pairs, give the product 65. These factors can also be negative. 65 is a special two-digit number because apart from 1 and 65, it has only one other double factor, i.e. 5 and 13. In this lesson, we will learn the factors of 65, prime factors. of 65 and the factors of 65 in pairs along with solved examples.

  • Elements of 65: 1, 5, 13 and 65
  • Prime factors of 65: 65 = 5 × 13

1. What is the factor of 65? 2. How to calculate the factor of 65? 3. Factors of 65 prime factors 4. Factors of 65 in pairs 5. FAQ about Factors of 65

What are the factors of 65?

Let’s first understand the meaning of the elements. A factor is that number that divides any given number without leaving a remainder at the end. The number 65 is said to be an odd composite number. A composite number is a number that includes more than two factors. For example, consider the number 65. The coefficients of 65 are 1, 5, 13, and 65.Read: What is the prime factor of 65

How to calculate the factor of 65?

Let’s start calculating the factors of 65. Let’s start with 1. Divide 65 by 1. The remainder is 0? Right! By factoring definition, the number 65 divides evenly by 1 without leaving a remainder.Read more: DTS Neo 2.5 | Q&A Next, try the number 2. Since 65 is odd, it cannot be divisible by 2 or multiple of 2. So we only need to check for odd numbers. Let’s try with the number 3. 65 ÷ 3 = 21.66 So 3 is not a factor of 65. Now let’s try with the number 5. To get a prime factor of 65, we divide it by the factor. Its smallest prime number is 5.

  • 65 5 = 13
  • 13 is a prime number whose factors are 1 and 13.
  • The process of factoring primes continues until we get a quotient of 1.
  • The prime factorization of 65 is shown below:
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Prime factor of 65The prime factors of 65 can also be expressed like this: Read more: 48 inches in feet Now that we have factored our numbers, we can multiply them and get other factors . Can you try and find out if all the elements are covered or not? And as you may have guessed, for prime numbers, there are no other factors.

  • The coefficients of 62 – The coefficients of 62 are, 1, 2, 31 and 62
  • The coefficients 63 – The coefficients 63 are 1, 3, 7, 9, 21 and 63
  • The coefficients of 69 – The coefficients of 69 are 1, 3, 23 and 69.
  • Factors of 66 – The factors of 66 are 1, 2, 3, 6, 11 and 66
  • Factories of 68 – The factors of 68 are 1, 2, 4, 17, 34 and 68

Challenging question:

  • Mike had to divide the 65 students in his class into different groups with an equal number of students in all groups. Each group must have more than one student and not all students may be in a group. How many ways can Mike form these groups?

Elements of 65 in pairs

  • The pair of numbers that give 65 when multiplied together is called a factor of 65.
  • Therefore, the pair of coefficients of 65 are (1,65) and (5,13).
  • Since the product of two negative numbers is positive, (-) × (-) = (+), (-1, -65), (-5, -13) are also factor pairs of 65.

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  • The numbers that we multiply by 65 are factors of 65.
  • The coefficients of 65 are 1, 5, 13, and 65.
  • Since 65 is an odd composite number, all its factors will also be odd.
  • The number 65 is neither a perfect square nor a perfect cube.
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