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Class 5 Maths Chapter 13 Notes Animal Jumps
Class 5 Maths Notes Chapter 13 – Class 5 Animal Jumps Notes
Multiples are the results of multiplying a given number by any other number like: 1, 2, 3, … Or we can say that they are the “skip counting” of a number.
For example, first three multiple of 4 are: 4 × 1 = 4, 4 × 2 = 8, 4 × 3 = 12.
Factors are numbers that divide a given number exactly, without leaving a remainder. When you multiply two (or more) numbers to get a product, those numbers are the factors of the product.
→ Every number is a multiple of itself.
→ The first multiple of any non-zero number is the number itself.
→ Multiples are always greater than or equal to the number itself.
→ There are an infinite number of multiples for any given number.
→ The smallest multiple of a number is the number itself.
→ The multiples of an even number are always an even number.
→ The multiples of an odd number are alternatively an odd and even numbers
→ 1 is a factor of every number.
→ A factor is always less than or equal to the number it divides.
→ Factors always exist in pairs.
→ Every number (except 0) has at least two factors: 1 and the number itself.
→ There are a finite number of factors of any number.
→ If a number has only factors then the number is prime.
→ The factors of a number is equal to or less than the given number.
→ Zero is not a factor of any number, whereas every number is a factor of zero.
→ Factors that two or more numbers share are known as common factors.
→ Multiples that two or more numbers share are known as common multiples.
→ If a number is divisible by another number, the second number is the factor of first number and first number is multiple of first number.
Factors
→ A factor of a given number is a number that divides the given number without leaving a remainder. e.g. The factors of 12 are 1,2,3,4,6 and 12.
Visualisation of Factors Using Arrays
→ We can use array diagrams to visualise the factors of the given number. An array is an arrangement of objects, numbers or shapes in rows (horizontal) and columns (verticals).
→ Each array represents a way to split the number evenly.
e.g. The different arrays for number 12 to visualise its factors are
So, all the factors of 12 are 1,2,3,4,6 and 12.
Common Factors
→ The common factors of the given two or more numbers are the numbers that divide all the given numbers without leaving any remainders.
→ e.g. The common factors of 12 and 9 are given as
Then, common factors = 1, 3.
Multiples
→ The multiples of a given number are the numbers obtained by multiplying the given number with any natural number (i.e. 1,2,3, ….. ).
→ e.g. The multiples of 4 are 4 × 1, 4 × 2, 4 × 3, 4 × 4, 4 × 5, …….
i.e. 4,8,12,16,20, ……..
Common Multiples
→ The common multiples of the given two or more numbers are the numbers that are the. multiples of all the given two or more numbers.
→ e.g. The common multiples of 3 and 6 are given as
Then, common multiples =6,12,18,24, ……..
Visualisation of Multiples and Common Multiples Using Number Line
→ We can use number lines to visualise the common multiples of given two numbers by making equal jumps for two numbers and then checking where both land together.
→ e.g. The visualisation of common multiples of 2 and 3 on number line is shown below
Clearly, common multiples of 2 and 3 are 6,12, ……..
Some Important Points
- 1 is the factor of every number but 1 is the multiple of 1 only.
- 0 is not a factor of any number but 0 is the multiple of every number.
- Every number except 1 has atleast two factors, i.e. 1 and the number itself.
- Every number is a multiple of itself.
- The consecutive numbers share no common factor except 1.
- 2 is the smallest factor of every even number, while 1 is the smallest factor of every odd number.
- 0 is the smallest even (non-negative) multiple of every number.