Mathematics is one of the subject areas in which students must master concepts. Thorough practice is one of the most important aspects of mastering mathematics, and the International Maths Olympiad (IMO) is one such platform where students are trained to understand its fundamentals. This article will give you detailed information about IMO Class 4 Chapter 3: Factors and Multiples.

International Maths Olympiad is held by School Connects Online. It is open to students in grades 1 to 10. All of the questions on these exams are multiple-choice. The Olympiad exam also serves as a foundation for students to achieve academic success. It gives students an advantage over their peers when solving difficult questions.

**IMO Class 4 Chapter 3: Factors and Multiples Detailed Notes**

In primary school, we learned a variety of mathematical concepts. The concepts of factors and multiples are crucial, particularly when working with reducing and expanding fractions. They are also utilized when looking for patterns in data. Let’s discuss the definition of multiples, common multiples, and the distinction between factors, and multiples with a lot of worked examples in this article.

**What are Multiples?**

A multiple is an outcome of multiplying an integer (not a fraction) by a given number. By subtracting the product of counting numbers and whole numbers, the multiples of the whole number are obtained. For instance, we multiply 6 by 1, 6 by 2, 6 by 3, and so forth to find the multiples of 6. The result of this multiplication is multiples.

Example 1: | Find the multiples of whole number 3 | |||||||

Multiplication: | 3 x 1 | 3 x 2 | 3 x 3 | 3 x 4 | 3 x 5 | 3 x 6 | 3 x 7 | 3 x 8 |

Multiples of 3: | 3 | 6 | 9 | 12 | 15 | 18 | 21 | 24 |

Solution: | The multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24 … |

**List of Multiples of Numbers**

Since multiples of a number are created by multiplying it by natural numbers, a number can have an infinite number of multiples. So, for a given number, we can write an infinite number of multiples. The first 10 multiples of a few numbers are displayed in the table below.

Number | First 10 Multiples |

2 | 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 |

3 | 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 |

4 | 4, 8, 12, 16, 20, 24, 28, 32, 36, 40 |

5 | 5, 10, 15, 20, 25, 30, 35, 40, 45, 50 |

6 | 6, 12, 18, 24, 30, 36, 42, 48, 54, 60 |

7 | 7, 14, 21, 28, 35, 42, 49, 56, 63, 70 |

8 | 8, 16, 24, 32, 40, 48, 56, 64, 72, 80 |

9 | 9, 18, 27, 36, 45, 54, 63, 72, 81, 90 |

10 | 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 |

11 | 11, 22, 33, 44, 55, 66, 77, 88, 99, 110 |

12 | 12, 24, 36, 48, 60, 72, 84, 96, 108, 120 |

13 | 13, 26, 39, 52, 65, 78, 91, 104, 117, 130 |

14 | 14, 28, 42, 56, 70, 84, 98, 112, 126, 140 |

15 | 15, 30, 45, 60, 75, 90, 105, 120, 135, 150 |

16 | 16, 32, 48, 64, 80, 96, 112, 128, 144, 160 |

17 | 17, 34, 51, 68, 85, 102, 119, 136, 153, 170 |

18 | 18, 36, 54, 72, 90, 108, 126, 144, 162, 180 |

19 | 19, 38, 57, 76, 95, 114, 133, 152, 171, 190 |

20 | 20, 40, 60, 80, 100, 120, 140, 160, 180, 200 |

**Factors**

Their common factors are those that two or more numbers have in common. How then do we identify the commonalities? Think about the numbers A and B. Note the numbers that are shared by both A and B and all of the factors of A and B separately. Let’s use an illustration to better understand the idea of common factors.

Think about the identical two numbers, 30, and 45.

Factors of 30 and 45 are –

30 = {1, 2, 3, 5, 10, 15, and 30}

45 = {1, 3, 5, 9, 15, 45}

What common characteristics can you see? In both 30 and 45, 15, 5, 3, and 1 are present.

1, 3, 5, and 15 are frequent factors between 30 and 45.

There are numerous practical uses for this idea as well. Consider that you want to floor a space that is 30 m x 45 m in size. With the aid of common factors, the largest size of a square tile that can be used can be determined. A square tile with a side length of 15 cm should be used because 15 is the highest common factor.

**Frequently Asked Questions on Multiples**

**What are multiples?**

A number that is created by multiplying two other numbers is referred to as a multiple of that number.

**Are our products and multiples the same thing?**

The result of two numbers being multiplied is known as the product. We can say that the multiples of two numbers are another name for the product.

**Are there even multiples of four?**

The multiples of four are indeed even. Since 4, all of its multiples are even because it is an even number.

**Do multiples of three always equal multiples of six?**

Because 3 is a factor of 6, the multiples of 3 are also the multiples of 6.

**Also Read:** **How to prepare for Olympiads?**

School Connect Online offers olympiads such as

1. National Science Olympiad (NSO)

2. International Mathematics Olympiad (IMO)

4. Artificial Intelligence Olympiad.

Prepare for your Olympiad coaching with the Olympiad Genius by interacting with one of the greatest educators from IIT, NIT, as well as other institutions!

To know more: https://blog.schoolconnectonline.com/

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