Factors of 102
Factors of 102 are the numbers which when multiplied in pairs give the product as 102. These factors can be both positive and negative. The number 102 is the first 3-digit number divisible by the numbers 3, 6, 17, 34, and 51. In this lesson, we will calculate the factors of 102, prime factors of 102, and factors of 102 in pairs along with solved examples for a better understanding.
- Factors of 102: 1, 2, 3, 6, 17, 34, 51 and 102
- Prime Factorization of 102: 102 = 2 × 3 × 17
| 1. | What Are the Factors of 102? |
| 2. | How to Calculate Factors of 102? |
| 3. | Factors of 102 by Prime Factorization |
| 4. | Factors of 102 in Pairs |
| 5. | FAQs on Factors of 102 |
What are the Factors of 102?
Before we study about factors of 102, let's have a quick recall about "Factor". The number of factors is based on the type of number. A prime number is a number that consists of only two factors. A composite number is a number that has more than two factors. Coming back to number 102. Factors of 102 are 1, 2, 3, 6, 17, 34, 51, 102. Therefore, 102 is a composite number.
How to Calculate the Factors of 102?
To calculate the factors of 102, start with the smallest whole number 1. Divide 102 with the number 1. Is the remainder zero? Yes! By factor definition, the number is divided equally without leaving a remainder.
- 102 ÷ 1 = 102
- 102 × 1 = 102
We try with the next whole number 2. Is the remainder zero? Yes!
- 102 ÷ 2 = 51
- 51 × 2 = 102
Proceeding in a similar manner we get,
- 102 ÷ 3 = 34
- 3 × 34 = 102
Hence, the factors of 102 are 1, 2, 3, 6, 17, 34, 51 and 102.
Explore factors using illustrations and interactive examples
- Factors of 38 - The factors of 38 are 1, 2, 19 and 38
- Factors of 42 - The factors of 42 are 1, 2, 3, 6, 7, 14, 21 and 42
- Factors of 81- The factors of 81 are 1, 3, 9, 27 and 81
- Factors of 48 - The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48
- Factors of 168 - The factors of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84 and 168.
- Factors of 180 - The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90 and 180
Important Notes:
- Factors of 102 are 1, 2, 3, 6, 17, 34, 51 and 102.
- Only whole numbers and integers can be converted into factors.
- Only composite numbers can have more than two factors.
Prime factorization is a process of breaking down the composite number into its prime factors. To get the prime factorization of 102, we divide it by its smallest prime factor, which is 102 ÷ 2 = 51. Now 51 is divided by the prime number 3.
- 51 ÷ 3 = 17
The process of prime factorization continues till we get the quotient as 1. Therefore, factors of 102 by prime factorization are:
It can also be written as 102 = 2 × 3 × 17. Now that we have done the prime factorization of our number, we can multiply them and get the other factors. Can you try and find out if all the factors are covered or not? And as you might have already guessed, for prime numbers, there are no other factors.
Factors of 102 in Pairs
Pair factors are the factors of a number given in pairs when multiplied together give that original number. The pair factors of 102 would be the two numbers when multiplied together, result in the value 102. Also, factors of 102 can have negative pair factors as well.
Positive Pair Factors of 102 are:
- 1 × 102 = 102
- 2 × 51 = 102
- 3 × 34 = 102
Positive Pair Factors of 102 are (1, 102), (2, 51) and (3, 34).
Negative Pair Factors of 102 are:
- -1 × -102 = 102
- -2 × -51 = 102
- -3 × -34 = 102
Negative Pair Factors of 102 are (-1, -102), (-2, -51) and (-3, -34).
Challenging Questions:
- Can 0.51 be a factor of 102?
- Is 3/17 a factor of 102?
FAQs on Factors of 102
What are the factors of 102?
The factors of 102 are 1, 2, 3, 6, 17, 34, 51 and 102.
What is the highest factor of 102?
102 is the highest factor of 102. Every number is the highest factor of itself.
Is 102 prime or composite?
The number 102 is composite since it has more than two factors.
What are the prime factors of 102?
The prime factors of 102 are 2, 3, and 17.
What are the common factors of 102 and 119?
The factors of 102 are 1, 2, 3, 6, 17, 34, 51 and 102. The factors of 119 are 1, 7, 17, and 119. Hence, the common factors are 1, 17 and 119.