Write 99 as a Product of Prime Factors
Factors of 99
Did you know that 99 is the sum of the cubes of three consecutive integers: 99 = 23 + 33 + 43? Also, 99 is an odd composite number. It comprises of factors other than 1 and itself. Let's learn about the factors of 99, factors of 99 in pairs, prime factorization of 99, prime factors of 99, and the factor tree of 99.
- Factors of 99:1, 3, 9, 11, 33, and 99
- Prime Factorization of 99: 3 × 3 × 11
| 1. | What Are the Factors of 99? |
| 2. | How to Calculate the Factors of 99? |
| 3. | Tips and Tricks |
| 4. | Factors of 99 by Prime Factorization |
| 5. | Factors of 99 in Pairs |
| 6. | Important Notes |
| 7. | FAQs on Factors of 99 |
What Are The Factors of 99?
- Factors of 99 are numbers which on dividing 99 leave no remainder.
- Example: We can use division to check whether 11 and 10 are factors of 99.
- 99 divides into 11 equal parts with no remainder. On dividing 99 into 11 parts we get a whole number, i.e., 9. Therefore, 11 is a factor of 99.
- 99 does not get divided by 10 into equal whole parts. On dividing 99 into 10 parts, we get a fractional number, i.e., 9.9. Therefore, 10 is not a factor of 99.
- Since 99 is a composite number, it will have more than two factors. 99 has a total of 12 factors.
Explore factors using illustrations and interactive examples
- Factors of 33: The factors of 33 are 1, 3, 11, and 33.
- Factors of 75: The factors of 75 are 1, 3, 5, 25, and 75.
- Factors of 6: The factors of 6 are 1, 2, 3, and 6.
- Factors of 98: The factors of 98 are 1, 2, 7, 14, 49, and 98.
- Factors of 72: The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.
How To Calculate Factors of 99?
There are two common methods to find the factors of 99: Division method and Prime factorization method .Let us calculate factors of 99 using the division method.
- While considering numbers that can divide 99 without remainders, we start with 1, then check 2, 3, 4, 5, 6, 7, 8, 9, 2, 3, 4, 5, 6, 7, 8, 9, etc. up to 45 (which is almost half of 99).
- 99 ÷ 1 = 99, Remainder = 0
- 99 ÷ 3 = 33, Remainder = 0
- 99 ÷ 9 = 11, Remainder = 0
- 99 ÷ 11 = 9, Remainder = 0
Tips and Tricks
- 99 = 3 × 3 × 11 = 32× 11
- To get the total numbers of factors of 99, simply add one to the exponent 2 and 1 and multiply their sums. (2 + 1) x (1 + 1) = 3 x 2 = 6
- Factors of 99 = 1, 3, 9, 11, 33, and 99
Factors of 99 by Prime Factorization
Prime factorization is to express a composite number as the product of its prime factors. A factor tree is a special branching diagram where we find the factors of a number, then the factors of those numbers, and so on until we cannot factor anymore. The ends of a factor tree are all the prime factors of the original number.
Factors of 99 in Pairs
Pair factors of the number 99 are the whole numbers which multiply to get the original number, i.e., 99. Pair factors could be either positive or negative but not a fraction or decimal number.
There are 6 factor pairs of 99, and they are (1, 99), (-1, -99), (3, 33), (-3, -33), (9, 11), and (-9, -11).
Important Notes
- 99 is a composite number.
- 3 and 11 are the only prime numbers that are factors of 99.
- The number of factors of a given number is finite; 99 has a total of 6 factors.
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Example 1:Emma asks her students to give her the product of all the unique prime factors of the number 99. If the students give the correct answer, what must have been their answer?
Solution:
Prime factors of 99 are 3 and 11.
Product of these prime factors = 3 x 11 = 33
The product of all the prime factors of the number 99 is 33.
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Example 2:Jason is trying to calculate the mean of all the factors of 99. He is a bit confused; can you help him with the same?
Solution:
Factors of 99: 1, 3, 9, 11, 33, and 99
Sum of all the given factors = 1 + 3 + 9 + 11 + 33 + 99 = 156
To calculate the mean, we will divide the sum of the factors with the total numbers of factors, i.e., 6. 156 ÷ 6 = 26
Thus mean of all the factors of 99 = 26
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FAQs on Factors of 99
What are the factors of 99?
The factors of 99 are 1, 3, 9, 11, 33, and 99.
What are the common factors of 99 and 36?
The factors of 99 are 1, 3, 9, 11, 33, and 99.
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
The common factors are 1, 3, and 9.
What are the prime factors of 99?
The prime factors of 99 are 3 and 11.
What are the factors of 99 and 98?
The factors of 99 are 1, 3, 9, 11, 33, and 99.
The factors of 98 are 1, 2, 7, 14, 49, and 98.
What are the factor pairs of 99?
The factor pairs of 99 are (1, 99), (3, 33), and (9, 11).
Write 99 as a Product of Prime Factors
Source: https://www.cuemath.com/numbers/factors-of-99/
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