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Chapter 2: Problem 12

List all the factors of each number. $$ 13 $$

Short Answer

Expert verified
The factors of 13 are 1 and 13.

Step by step solution

01

Understand the Definition of Factors

Factors of a number are integers that divide the number exactly without leaving a remainder. For instance, if a factor divides 13 evenly, there will be no remainder.
02

Find the Factors of 13

To find the factors of 13, begin by considering the smallest factor, which is always 1. Next, test integers greater than 1 by dividing them into 13 to see if they leave any remainder.
03

Identify Divisors

Divide 13 by each integer starting from 1 up to 13. Specifically: - 13 梅 1 = 13 (No remainder)- 13 梅 2 = 6.5 (Not an integer, remainder present)- 13 梅 3 through 13 梅 12 (All divisions result in a remainder)- 13 梅 13 = 1 (No remainder)
04

List the Factors

Based on the calculations, the divisors without remainders are 1 and 13. Hence, the factors of 13 are 1 and 13.

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Key Concepts

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

Integer Division
Integer division is a process where one integer is divided by another, resulting in a quotient and possibly a remainder. For example, if we divide 13 by 2, it goes 6 times and leaves a remainder. This is written as 13 梅 2 = 6 R1.

To conduct integer division:
  • Divide the numbers.
  • Ignore decimals or fractions.
  • Note the remainder, if any.
Integer division is key when finding factors, as factors divide the number exactly without a remainder.
Remainders
Remainders occur when an integer does not divide evenly into another. For instance, 13 梅 2 leaves a remainder of 1. This indicates that 2 is not a factor of 13 since the division isn鈥檛 exact.

A factor must divide a number completely, leaving no remainder. While checking for factors of 13, you would find that most divisions leave remainders, except for when divided by 1 and 13.
Mathematical Factors
Mathematical factors are numbers you can multiply together to obtain another number. For example, 1 and 13 are factors of 13 because 1 脳 13 equals 13.

To determine factors of a number:
  • Start with 1 and the number itself.
  • Test each number in between to see if they divide evenly.
  • Only include numbers that divide without a remainder.
For 13, the only numbers that fulfill these criteria are 1 and 13, making them the factors of 13.

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