Multiples of 21

Created by: Team Maths - Examples.com, Last Updated: May 23, 2024

Multiples of 21

Multiples of 21 are the numbers you get when you multiply 21 by any integer. These numbers form a sequence where each term is a product of 21 and an integer, such as 21, 42, 63, and so on. Multiples of 21 are part of basic arithmetic and play a crucial role in understanding concepts like multiplication, factors, and divisors. By identifying these multiples, students can better grasp the relationships between numbers and how they interact through multiplication. Understanding multiples also helps in solving various maths problems related to divisibility and number patterns.

What are Multiples of 21?

Multiples of 21 are numbers obtained by multiplying 21 by any integer. Examples include 21, 42, 63, 84, and so on. These multiples are integral in understanding factors, divisors, and patterns in arithmetic.

Prime factorization of 21: 21 = 3 × 7 First 10 multiples of 21: 21, 42, 63, 84, 105, 126, 147, 168, 189, 210.

Table of 21

Important Notes

Definition: Multiples of 21 are the products of 21 and any integer. In other words, a number n is a multiple of 21 if there exists an integer k such that n = 21×kn.

Identification: To identify if a number is a multiple of 21, divide the number by 21. If the result is an integer with no remainder, the number is a multiple of 21.

First Few Multiples: The first few multiples of 21 are 21, 42, 63, 84, 105, 126, 147, 168, 189, and 210.

Properties:

• Even Distribution: Multiples of 21 are evenly spaced by 21 units.
• Divisibility: A multiple of 21 is always divisible by both 3 and 7, since 21 = 3×7.

Applications:

Common Multiples: Finding common multiples of 21 with other numbers can be useful in solving least common multiple (LCM) problems.

Patterns: Understanding multiples of 21 can help in recognizing numerical patterns and sequences in mathematics.

Examples: For example, 42, 84, and 126 are all multiples of 21 because 21×2 = 42, 21×4 = 84, and 21×6 = 126. Conversely, a number like 100 is not a multiple of 21 because 100÷21 does not result in an integer.

Examples on Multiples of 21

Example 1:

• Calculation: 21×1
• Result: 21
• Explanation: The first multiple of 21 is 21 itself.

Example 2:

• Calculation: 21×4
• Result: 84
• Explanation: Multiply 21 by 4 to get the fourth multiple of 21, which is 84.

Example 3:

• Calculation: 21×7
• Result: 147
• Explanation: Multiply 21 by 7 to get the seventh multiple of 21, which is 147.

Example 4:

• Calculation: 21×10
• Result: 210
• Explanation: Multiply 21 by 10 to get the tenth multiple of 21, which is 210.

Example 5:

• Calculation: 21×12
• Result: 252
• Explanation: Multiply 21 by 12 to get the twelfth multiple of 21, which is 252.

Verification of Multiples

To verify if a number is a multiple of 21, divide the number by 21 and check if the remainder is zero.

Example 6:

• Number: 189
• Calculation: 189÷21 = 9
• Remainder: 0
• Explanation: Since the remainder is 0, 189 is a multiple of 21.

Example 7:

• Number: 250
• Calculation: 250÷21 = 11
• Remainder: 19
• Explanation: Since the remainder is 19, 250 is not a multiple of 21.

What are the first five multiples of 21?

The first five multiples of 21 are 21, 42, 63, 84, and 105.

How can I determine if a number is a multiple of 21?

To determine if a number is a multiple of 21, divide the number by 21. If the quotient is an integer and the remainder is 0, the number is a multiple of 21.

Is 210 a multiple of 21?

Yes, 210 is a multiple of 21 because 210÷21 = 10, which is an integer.

What is the 10th multiple of 21?

The 10th multiple of 21 is 21×10 = 210.

Are all multiples of 21 also multiples of 7 and 3?

Yes, because 21 is 7×3, any multiple of 21 is also a multiple of both 7 and 3.

How do I find the next multiple of 21 after a given multiple?

To find the next multiple of 21, add 21 to the given multiple. For example, after 84, the next multiple is 84+21 = 105.

Is 154 a multiple of 21?

No, 154 is not a multiple of 21 because 154÷21 = 7, meaning there is a remainder of 7.

Can a negative number be a multiple of 21?

Yes, negative numbers can be multiples of 21. For example, -21, -42, and -63 are all multiples of 21.

What is the smallest multiple of 21 greater than 100?

The smallest multiple of 21 greater than 100 is 105.

How are multiples of 21 used in real life?

Multiples of 21 can be used in various contexts such as dividing groups evenly, scheduling events, or solving problems in number theory and algebra.

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