# Multiples of 42

Created by: Team Maths - Examples.com, Last Updated: May 28, 2024

## Multiples of 42

In mathematics, multiples of 42 are the products obtained by multiplying the integer 42 with other integers. These numbers form a sequence where each term is a result of 42 times a whole number. Understanding multiples is essential in various mathematical concepts, such as finding common multiples, divisors, and factors. Multiples of 42 help in solving problems related to number theory and arithmetic operations. Identifying these multiples can aid in simplifying complex multiplication and division problems.

## What are Multiples of 42?

Multiples of 42 are the numbers you get when you multiply 42 by integers. These include 42, 84, 126, 168, 210, and so on. Essentially, any number that can be expressed as 42n, where n is an integer, is a multiple of 42.

Prime Factorization of 42: 2 × 3 × 7 First 10 Multiples of 42 are 42, 84, 126, 168, 210, 252, 294, 336, 378, 420.

Table of 42

## Important Notes

• Definition: Multiples of 42 are numbers that can be expressed as 42n, where n is any integer. Examples include 42, 84, 126, and so on.
• Divisibility: Every multiple of 42 is divisible by both 6 and 7 since 42 is the product of these numbers (42 = 6 × 7).
• Even Nature: All multiples of 42 are even numbers because 42 is an even number.
• Arithmetic Progression: The sequence of multiples of 42 forms an arithmetic progression with the first term being 42 and the common difference also being 42 (e.g., 42, 84, 126, 168).
• Common Multiples: Multiples of 42 can also be multiples of other numbers, especially those that are factors of 42, such as 2, 3, 6, 7, and 21.

## Examples on Multiples of 42

• 42×1 = 42
• 42×2 = 84
• 42×3 = 126

• 42×10 = 420
• 42×20 = 840
• 42×30 = 1260

### Real-Life Examples

• Weeks in a Year: There are 52 weeks in a year, which is not a multiple of 42, but considering every 6 weeks and adding one week gives us 42 days, aligning with 6 weeks. Therefore, 42 days (6 weeks) is a useful multiple in planning and scheduling.
• Event Planning: For a conference occurring every 42 days, the pattern helps in organizing recurring events (42 days = 1 cycle, thus 84 days = 2 cycles, etc.).

## Practical Examples of Multiples of 42

### What is the 15th multiple of 42?

The 15th multiple of 42 is 42×15 = 630.

### Is 378 a multiple of 42?

Yes, 378 is a multiple of 42 because 42×9 = 378.

### What is the next multiple of 42 after 420?

The next multiple of 42 after 420 is 420+42 = 462.

### Find the 25th multiple of 42.

The 25th multiple of 42 is 42×25 = 1050.

### Is 1001 a multiple of 42?

No, 1001 is not a multiple of 42 because 1001 cannot be expressed as 42×n for any integer n.

## What are multiples of 42?

Multiples of 42 are numbers obtained by multiplying 42 by any integer. Examples include 42, 84, 126, 168, and so on.

## How can you determine if a number is a multiple of 42?

To determine if a number is a multiple of 42, divide the number by 42. If the result is an integer without a remainder, the number is a multiple of 42.

## What is the first multiple of 42?

The first multiple of 42 is 42 itself, as it is 42 multiplied by 1.

## Are all multiples of 42 even numbers?

Yes, all multiples of 42 are even numbers because 42 is an even number, and the product of an even number and any integer is always even.

## What are the first five multiples of 42?

The first five multiples of 42 are 42, 84, 126, 168, and 210.

## How are multiples of 42 related to factors and divisors?

Multiples of 42 share 42 as a common factor. Therefore, 42 is a divisor of all its multiples.

## What is the least common multiple (LCM) of 42 and another number?

The least common multiple of 42 and another number is the smallest number that is a multiple of both 42 and the other number. To find it, you can use the prime factorization method.

## How do multiples of 42 relate to multiplication tables?

Multiples of 42 can be found in the 42 times table, where each entry is the product of 42 and a counting number (e.g., 42 × 1, 42 × 2).

## Can negative numbers be multiples of 42?

Yes, negative numbers can be multiples of 42. For example, -42, -84, and -126 are all multiples of 42.

## What is the 10th multiple of 42?

The 10th multiple of 42 is 420, as it is obtained by multiplying 42 by 10 (42 × 10).

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