What Are the Factors of 35: In this tutorial, we will explain what factors are, how to find the factors of the number 35, and provide examples to help you understand the process. Factors are numbers that can divide a given number exactly without leaving a remainder.

What Are Factors?

Factors of a number are the integers that can be multiplied together to produce the original number. For example, if two numbers multiply to give 35, then those two numbers are considered factors of 35. Factors come in pairs, and they include both the divisor and the quotient.

Steps to Find the Factors of 35

Follow these steps to find all the factors of 35:

  • Step 1: Start with the number 1. Since 1 is a factor of every number, it is always included. We know that \( 1 \times 35 = 35 \), so both 1 and 35 are factors.
  • Step 2: Check for the next integers up to the square root of 35. The square root of 35 is approximately 5.9, so we need to check integers from 1 to 5.9 to see if they divide 35 without a remainder.
  • Step 3: Identify other factors. Check if each integer from 2 to 5 divides 35 exactly (without leaving a remainder). If it does, both the integer and the corresponding quotient are factors.
  • Step 4: List all factor pairs. Once all divisors have been found, list the factor pairs for 35.

Finding the Factors of 35

Let’s apply the steps to find all factors of 35:

  • Step 1: Start with 1. Since \( 1 \times 35 = 35 \), the factors include 1 and 35.
  • Step 2: Check the next integers up to the square root of 35 (which is approximately 5.9). The integers to check are 2, 3, 4, and 5.
  • Step 3: Check each integer:
    • 2 does not divide 35 exactly, so it is not a factor.
    • 3 does not divide 35 exactly, so it is not a factor.
    • 4 does not divide 35 exactly, so it is not a factor.
    • 5 divides 35 exactly, as \( 5 \times 7 = 35 \). Therefore, both 5 and 7 are factors.
  • Step 4: The factors of 35 are 1, 5, 7, and 35.

Factor Pairs of 35

Factor pairs are pairs of numbers that, when multiplied together, give the original number. For 35, the factor pairs are:

  • \( 1 \times 35 = 35 \)
  • \( 5 \times 7 = 35 \)

Conclusion

Finding the factors of a number involves identifying all the numbers that divide it exactly. For 35, the factors are 1, 5, 7, and 35. These factors come in pairs that, when multiplied, produce the original number.