Factors

Factors of 102 | Prime Factorization of 102 | Factor Tree of 102

Written by Prerit Jain

Updated on: 05 Dec 2023

Factors of 102

Calculate Factors of

The Factors are

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What are the factors of 102

To find the factors of 102, we need to find all the numbers that divide into 102 without leaving a remainder. Here’s how we can do that:

2. Divide 102 by the smallest prime factor, which is 2. 102 divided by 2 is 51.
3. Divide 51 by the smallest prime factor, which is 3. 51 divided by 3 is 17.
4. Divide 17 by the smallest prime factor, which is 17. 17 divided by 17 is 1.

Now we have a list of all the factors of 102: 1, 2, 3, 6, 17, 34, 51, and 102.

The factors of 102 can be organized into two groups: the proper factors, which are all the factors less than 102, and the improper factors, which are all the factors greater than 102. The proper factors of 102 are 1, 2, 3, 6, 17, 34, and 51. The improper factors of 102 are 102 and 204.

How to Find Factors of 102

Here are four methods that you can use to find the factors of 102:

• Factors of 102 using the Multiplication Method
• Factors of 102 using the Division Method
• Prime Factorization of 102
• Factor tree of 102

Factors of 102 Using the Multiplication Method

To find the factors of 102 using the multiplication method, we can start with the number 1 and then keep finding the next smallest numbers that are factors of 102. We can do this by dividing 102 by each of the factors we have already found and checking if the result is also a factor.

For example, we can start with the number 1, which is always a factor of every number. Then, we can divide 102 by 1 to get 102, which is also a factor. Next, we can divide 102 by 2 to get 51, which is also a factor. We can keep doing this until we have found all the factors of 102.

Using the multiplication method, we can find that the factors of 102 are 1, 2, 3, 6, 17, 34, 51, and 102.

Factors of 102 through Division Method

The “division method” for finding the factors of a number is a way to find all the pairs of numbers that multiply together to equal the number by dividing the number by each of its factors. Here’s how we can use the division method to find the factors of 102:

2. Divide 102 by each number to see if it is a factor. For example, we can divide 102 by 1 to get 102. 102 is a factor of 102, so 1 is also a factor.
3. Divide 102 by each number to see if it is a factor. For example, we can divide 102 by 2 to get 51. 51 is a factor of 102, so 2 is also a factor.
4. Divide 102 by each number to see if it is a factor. For example, we can divide 102 by 3 to get 34. 34 is a factor of 102, so 3 is also a factor.
5. Divide 102 by each number to see if it is a factor. For example, we can divide 102 by 6 to get 17. 17 is a factor of 102, so 6 is also a factor.
6. Divide 102 by each number to see if it is a factor. For example, we can divide 102 by 17 to get 6. 6 is a factor of 102, so 17 is also a factor.
7. Divide 102 by each number to see if it is a factor. For example, we can divide 102 by 34 to get 3. 3 is a factor of 102, so 34 is also a factor.
8. Divide 102 by each number to see if it is a factor. For example, we can divide 102 by 51 to get 2. 2 is a factor of 102, so 51 is also a factor.

Using the division method, we can see that the factors of 102 are 1, 2, 3, 6, 17, 34, 51, and 102.

Prime Factorization of 102

Calculate Prime Factors of

The Prime Factors of 102 =

2 x

3 x

17

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To find the prime factorization of 102, we need to find the prime factors of 102 and then list them in order. Prime factors are numbers that are only divisible by 1 and themselves.

To find the prime factors of 102, we can start by dividing 102 by the smallest prime factor, which is 2. The result, 51, is not a prime number, so we can divide it by the next smallest prime factor, which is 3. The result, 17, is a prime number, so we can divide it by the next smallest prime factor, which is 17. The result, 1, is not a prime number, so we have found all the prime factors of 102.

The prime factors of 102 are 2, 3 and 17, so the prime factorization of 102 is 2 x 3x 17.

Factor tree of 102

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A factor tree is a way to find the prime factors of a number by breaking it down into smaller and smaller factors until we reach the prime factors. Here’s how we can use a factor tree to find the prime factorization of 102:

• Find two numbers that multiply together to equal 102. These are called “factors.” Some possible pairs of factors are (1, 102), (2, 51), (3, 34), and (6, 17). Let’s try (2, 51).
• Write the number 102 as the product of 2 and 51. This looks like this: 102 = 2 x 51.

Now, we need to find the prime factors of 2 and 51. 2 is already a prime number, so its prime factors are just 1 and 2. 51 can be written as the product of 3 and 17, like this: 51 = 3 x 17.

• 3 and 17 are both prime numbers, so their prime factors are just 1 and themselves.
• We can now write the prime factorization of 102. This is the list of all the prime factors of 102, written in order. The prime factorization of 102 is 2 x 3 x 17.

Using a factor tree, we can see that the prime factors of 102 are 2, 3and 17.

Factor Pairs of 102

Calculate Pair Factors of

1 x 102=102

2 x 51=102

3 x 34=102

6 x 17=102

17 x 6=102

34 x 3=102

51 x 2=102

So Pair Factors of 102 are

(1,102)

(2,51)

(3,34)

(6,17)

(17,6)

(34,3)

(51,2)

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The factor pairs of 102 are the pairs of numbers that multiply together to equal 102. For example, some of the factor pairs of 102 are (1, 102), (2, 51), (3, 34), and (6, 17).

The factor pairs of 102 can be organized into two groups: the pairs where both numbers are less than 102, and the pairs where one number is greater than 102 and the other is less than 102. The pairs where both numbers are less than 102 are called the “proper factor pairs” of 102, and the pairs where one number is greater than 102 and the other is less than 102 are called the “improper factor pairs” of 102.

Factors of 102 – Quick Recap

• Factors of 102: 1, 2, 3, 6, 17, 34, 51, and 102.
• Negative Factors of 102: -1,- 2,- 3, -6, -17, -34, -51, and -102.
• Prime Factors of 102:  2, 3, and 17.
• Prime Factorization of 102: 2, 3, and 17.

Factors of 102 – Fun Facts

• The factors of 102 can be organized into two groups: the proper factors, which are all the factors less than 102, and the improper factors, which are all the factors greater than 102. The proper factors of 102 are 1, 2, 3, 6, 17, and 34. The improper factors of 102 are 102 and 204.
• The number of proper factors of 102 is 6, and the number of improper factors is 2. This means that there are a total of 8 factors of 102.
• The sum of the proper factors of 102 is 58, and the sum of the improper factors is 306.
• The product of the proper factors of 102 is 408, and the product of the improper factors is 20408.
• The proper factors of 102 can be organized into three pairs of factors that multiply together to equal 102. These pairs are (1, 102), (2, 51), and (3, 34).

Also Check: Multiples, Square Root, and LCM

Solved Examples of Factor of 102

Q.1: Daniel has 102 apples and wants to divide them evenly among 10 people. How many apples would each person get?
Solution: 102 ÷ 10 = 10 remainder 2. Dividing 102 by 10 gives a quotient of 10 and a remainder of 2. This means that each person would receive 10 apples, and there would be 2 apples remaining.

Q.2: John wants to split his 102 pencils evenly with his 5 cousins. How many pencils will each cousin receive?
Solution:
Each cousin will receive 20 pencils since 102 is divisible by 5 (102 ÷ 5= 20 and remainder 2) with 2 pencils remaining.

Q.3: Mary has a box containing 102 chocolate bars and wants to distribute them equally among 6 friends. How many chocolate bars will each friend get?
Solution:
102 ÷ 6 = 17. Dividing 102 by 6 gives a quotient of 17. Therefore, each friend will receive 17 chocolate bars.

Q.4: David needs to supply the same number of toys to 12 children. What is the fewest amount of toys he needs in order to accomplish this task?
Solution: To supply the same number of toys to 12 children, we need to find the least common multiple (LCM) of the numbers 12. The LCM of 12 is simply 12 itself, as it is the smallest number that is divisible by 12. Therefore, David needs a minimum of 12 toys in order to supply the same number of toys to 12 children.

Q.5: Joe has 101 books and 3 crates he wants to fill with an equal number of books in each crate. Is it possible for him to do this?
Solution:
No, it is not possible for him to do this since 101 books cannot be divided into 3 even parts since 101 is not divisible by 3.

Q.6: Susan has a stack of paper towels containing 108 sheets and wants them divided exactly into 4 stacks of 27 sheets each. Is this possible?
Solution:
Yes, this is possible as 108 sheets can be divided evenly into 4 parts with 27 sheets each in 4 stacks as 27 x 4 = 108.

Q.7: Tina wants to make 8 servings out of a cake recipe that calls for 104 grams of sugar. Is it possible?
Solution:
Yes, it is possible as 104 grams can be divided into 8 even parts using factors of 104 such as 13 x 8  (104÷13=8, 8×8 = 64 ).

Q.8: Bob has a collection of 110 coins which he plans on giving away in equal amounts among 11 relatives. Can he accomplish this task?
Solution:
Yes, Bob can accomplish this task as 110 coins can be divided evenly into 11 parts using factors like 10×11  (110÷10 = 11, 11×10 = 110 ).

Q.9: Sam has 105 gifts that need delivering but only 7 cars are available for delivery. Is there a way for Sam to still deliver all his gifts?
Solution:
Yes, Sam could still deliver all his gifts if he decides to use the factors of 105 such as 15 x 7 (105÷15=7, 7×15=105 ) that is he sends 15 gifts at a time by one car.

Frequently Asked Questions on Factors of 102

What is a factor of 102?

A factor of 102 is any number that can be divided into 102 with no remainders. The factors of 102 include 1, 2, 3, 6, 17, 34, 51, and 102.

How many factors does the number 102 have?

The number 102 has 8 factors including 1, 2, 3, 6, 17, 34, 51, and 102.

What is the greatest common factor of 102 and 204?

The greatest common factor of 102 and 204 is 102 since both numbers are divisible by 102

What is the least common multiple for 24, 40, and 60?

The least common multiple for 24, 40, and 60 is 120 since all three numbers are divisible by 120 (8 x 3 x 5= 120).

Can 101 be a factor of any number?

No, 101 cannot be divided evenly into any number because 101 itself is not a factor of any number.

What is the prime factorization for the number 102?

The prime factorization for 102 is 2 x 3 x 17 since 114 can only be equally divided by these three primes numbers.

How many even numbers are among the list of factors for 95?

The factors of 95 are: 1, 5, 19, and 95.None of the factors of 95 are divisible by 2, so there are no even numbers among the list of factors for 95.

Are 55 and 75 part of the list of factors for 104?

No, 55 and 75 does not belong in the list of factors for 104 as they both are unable to divide evenly into them.

Written by by

Prerit Jain

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