Multiples

# What are the Multiples of 34 | All Multiples of 34 up to 1000

Written by Prerit Jain

Updated on: 12 Aug 2023

### What are the Multiples of 34 | All Multiples of 34 up to 1000

The first ten multiples of 34 are listed as follows: 34, 68, 102, 136, 170, 204, 238, 272, 306, and 340.

The multiples of 34 are a sequence of numbers that can be obtained by multiplying the number 34 with a sequence of natural numbers.

The difference between any two consecutive numbers in the sequence of multiples of 34 is always 34.

To find the multiples of 34, you need to perform a repeated addition of the number 34 or multiply the number 34 with a sequence of natural numbers.

Alternatively, the multiples of 34 are the numbers that when divided by 34 do not leave any remainder.

## What are the first five multiples of 34

To find the first five multiples of 34, we can use a method listed below:.

Step 1: To find the first multiple of 34, multiply 34 by 1. 34 x 1 = 34.

Step 2: To find the second multiple of 34, multiply 34 by 2. 34 x 2 = 68. Alternatively, you can add 34 to the first multiple to get the second multiple of 34. 34 + 34 = 68.

Step 3: Multiply 34 by 3 to get the third multiple of 34. 34 x 3 = 102. Alternatively, you can add 34 two times to the second multiple to get the third multiple of 34. 68 + 34 = 102.

Step 4: The fourth multiple of 34 can be found by multiplying 34 by 4. 34 x 4 = 136. Alternatively, you can add 34 three times to the third multiple to get the fourth multiple of 34. 102 + 34 = 136.

Step 5: To find the fifth multiple of 34, you need to multiply 34 by 5. 34 x 5 = 170. Alternatively, you can add 34 four times to the fourth multiple to get the fifth multiple of 34. 136 + 34 = 170.

Therefore, the first 5 multiples of 34 are 34, 68, 102, 136, and 170.

## How to find the Multiples of 34

To find the multiples of 34 we can use either of two methods which are most commonly used in finding the multiples of any number. The two methods are repeated addition and multiplication method.

### Finding multiples of 34 using the repeated addition method

We can obtain the multiples of 34 by adding 34 to itself repeatedly. The first multiple of 34 is 34 itself. To find the second multiple of 34, we add 34 to the first multiple, which gives 68. Continuing this process, we can obtain the third, fourth, and so on multiples of 34. An example of the first five multiples of 34 using the repeated addition method is given below:

34

34 + 34 = 68

68 + 34 = 102

102 + 34 = 136

136 + 34 = 170

### Finding the multiples of 34 using the multiplication method

The multiplication method can also be used to find the multiples of 34. To do this, we need to multiply the number 34 by a sequence of natural numbers. For example, to find the first five multiples of 34 using the multiplication method, we need to multiply 34 by 1, 2, 3, 4, and 5. The detailed steps are given below:

Step 1: To find the first multiple of 34, multiply 34 by 1. 34 X 1 = 34.

Step 2: To find the second multiple of 34, multiply 34 by 2. 34 X 2 = 68.

Step 3: Multiply 34 by 3 to get the third multiple of 34. 34 X 3 = 102.

Step 4: The fourth multiple of 34 can be found by multiplying 34 by 4. 34 X 4 = 136.

Step 5: To find the fifth multiple of 34, multiply 34 by 5. 34 x 5 = 170.

Hence the first 5 multiples of 34 are 34, 68, 102, 136, and 170. The multiplication method is a simple and efficient way to find multiples of any number, including 34.

## Finding the first 20 multiples of 34

To find the first 20 multiples of 34 using the multiplication method, you can follow similar steps. Create a table with the sequence of numbers from 1 to 20 and multiply 34 with each number in the sequence. The first 20 multiples of 34 are given below:

## Difference between Multiples and Factors of 34

In mathematics multiples and factors are two very different concepts.

To summarize, multiples of 34 are obtained by multiplying 34 by any integer, whereas factors of 34 are numbers that divide 34 exactly without leaving any remainder. It’s worth noting that every multiple of 34 is a multiple of 2.

## Solved Examples for Multiples of 34

1. What is the 10th multiple of 34?

To find the 10th multiple of 34, we simply multiply 34 by 10. So, the 10th multiple of 34 is 340.

1. Is 986 a multiple of 34?

Solution: To check if 986 is a multiple of 34, we need to divide 986 by 34. If the division gives us a whole number without a remainder, then 986 is a multiple of 34. In this case, 986 divided by 34 gives us 29 with a remainder of 18. Therefore, 986 is not a multiple of 34.

1. Write down the first five multiples of 34 that are greater than 200.

Solution: To find the first five multiples of 34 that are greater than 200, we can start by dividing 200 by 34 to see how many multiples we have before 200. We get 5 with a remainder of 30. So, we already have 5 multiples of 34 before 200. To find the next five multiples, we simply add 34 to 200 and continue doing so until we have five more multiples. The first five multiples of 34 that are greater than 200 are: 204, 238, 272, 306, and 340.

1. What is the sum of the first 15 multiples of 34?

To find the sum of the first 15 multiples of 34, we can use the formula for the sum of an arithmetic series. The first term is 34 and the common difference is also 34 since each term is obtained by adding 34 to the previous term. The formula is:

S = n/2 × [2a + (n – 1)d]

where S is the sum of the series, n is the number of terms, a is the first term, and d is the common difference. Substituting the values, we get:

S = 15/2 × [2(34) + (15 – 1)34]

S = 15/2 × [68 + 14 × 34]

S = 15/2 × 590

S = 4425

Therefore, the sum of the first 15 multiples of 34 is 4425.

1. What is the smallest positive multiple of 34 that is also a multiple of 51?

To find the smallest positive multiple of 34 that is also a multiple of 51, we need to find the least common multiple (LCM) of 34 and 51. The prime factorization of 34 is 2 × 17, and the prime factorization of 51 is 3 × 17. The LCM is the product of the highest powers of each prime factor. So, the LCM of 34 and 51 is:

LCM = 2 × 3 × 17

LCM = 102

Therefore, the smallest positive multiple of 34 that is also a multiple of 51 is 102.

## FAQs on Multiples of 34

### What is the next multiple of 34 after 102?

To find the next multiple of 34 after 102, we can add 34 to 102. The answer is 136.

### Is 34 a multiple of 17?

Yes, 34 is a multiple of 17 because 34 divided by 17 equals 2 with no remainder.

### What is the sum of the first 20 multiples of 34?

To find the sum of the first 20 multiples of 34, we can use the formula for the sum of an arithmetic series. The answer is 11,060.

### What is the largest factor of 34?

The largest factor of 34 is 34 because every number is a factor of itself.

### How many multiples of 34 are there between 100 and 500?

To find the number of multiples of 34 between 100 and 500, we can divide the difference between 100 and 500 (which is 400) by 34 and round up to the nearest whole number. The answer is 12.

Written by by

Prerit Jain

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