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Chapter 1: Problem 1

Find the greatest common divisor of 15 and 35 .

Short Answer

Expert verified
The greatest common divisor of 15 and 35 is 5.

Step by step solution

01

- List the Factors of Each Number

First, list all the positive factors for each number. Factors of 15 are 1, 3, 5, and 15. Factors of 35 are 1, 5, 7, and 35.
02

- Identify the Common Factors

Next, identify the common factors from the lists in Step 1. The common factors of 15 and 35 are 1 and 5.
03

- Select the Greatest Common Factor

Finally, select the largest number from the common factors identified in Step 2. The greatest common factor of 15 and 35 is 5.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Factors
Factors are numbers that divide exactly into another number. In other words, when you divide one number by its factor, the result is a whole number without any remainder. For example, the factors of 15 are the numbers that can divide 15 evenly, which are 1, 3, 5, and 15.
The process to find factors is quite simple:
  • Start with the number 1 and go up to the number itself.
  • Check each number to see if it divides evenly without a remainder.
So, for 15, we check: 1 (yes), 2 (no), 3 (yes), 4 (no), 5 (yes), and finally 15 (yes). Therefore, we have all the factors: 1, 3, 5, and 15.
Common Factors
Common factors are the factors that two or more numbers share. Identifying common factors involves comparing the list of factors from different numbers and finding the ones that appear in each list. Let's take the numbers 15 and 35 as an example:
Factors of 15: 1, 3, 5, 15
Factors of 35: 1, 5, 7, 35

The common factors are the numbers that appear in both lists. Here, 1 and 5 are the common factors. This means both 15 and 35 can be evenly divided by 1 and by 5.
Greatest Common Factor
The Greatest Common Factor (GCF) is the largest number that is a common factor of two or more numbers. It is the highest number that can divide each of the given numbers without a remainder. Finding the GCF is helpful in simplifying fractions and solving problems involving ratios.

To find the GCF of 15 and 35, we need to follow a few steps:
  • List the factors of each number.
  • Identify the common factors.
  • Choose the largest number from the common factors.
As seen earlier: Common factors of 15 and 35 are 1 and 5.
The greatest one among them is 5. So, the GCF of 15 and 35 is 5!

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Most popular questions from this chapter

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