Q: What is the total or count of factors of the number 105,135,300?
A: 144
How do I find the total factors of the number 105,135,300?
Step 1
Find the prime factorization of the number 105,135,300.
Use a factor tree to assist with solving. Take a look at our prime factorization page for additional help.
Factor Tree| 105,135,300 | |||||||||
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| 2 | 52,567,650 | ||||||||
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| 2 | 26,283,825 | ||||||||
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| 3 | 8,761,275 | ||||||||
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| 3 | 2,920,425 | ||||||||
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| 3 | 973,475 | ||||||||
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| 5 | 194,695 | ||||||||
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| 5 | 38,939 | ||||||||
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| 23 | 1,693 |
The prime factorization in exponential form is: 22 x 33 x 52 x 231 x 1,6931
Step 2
Setup the equation for determining the number of factors or divisors. The equation is:
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Where d(n) is equal to the number of divisors of the number and a, b, etc. are equal to the exponents of the prime factorization.
Now substitute the letters in the equation with the the exponents of your prime factorization and then solve to calculate the total number of divisors.
105,135,300 = 22 x 33 x 52 x 231 x 1,6931
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
d(105135300) = (2 + 1)(3 + 1)(2 + 1)(1 + 1)(1 + 1)
d(105135300) = (3)(4)(3)(2)(2)
d(105135300) = 144
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
d(105135300) = (2 + 1)(3 + 1)(2 + 1)(1 + 1)(1 + 1)
d(105135300) = (3)(4)(3)(2)(2)
d(105135300) = 144
More numbers for you to try
Take a look at the factors page to see the factors of 105,135,300 and how to find them.
Try the factor calculator.
Explore more about the number 105,135,300:
General Questions
- How is the number 105,135,300 written in scientific notation?
- What is the absolute value of the number 105,135,300?
- What is the negative version of the number 105,135,300?
- What is the place value chart for the number 105,135,300?
- What is the digital root of the number 105,135,300?
- How many digits is in the number 105,135,300?
Factoring Questions
- What are the factors or divisors of the number 105,135,300?
- What are the prime factors of the number 105,135,300?
- What is the total number of factors of the number 105,135,300?
- What is the total number of prime factors of the number 105,135,300?
- What is the sum of all factors of the number 105,135,300 including 105,135,300?
- What is the sum of all factors of the number 105,135,300 excluding 105,135,300?
- What are the factor combinations of the number 105,135,300?
- What is the prime factorization of the number 105,135,300?
Calculation Questions
Miscellaneous Questions
- How much data will 105,135,300 bytes hold in different storage units?
- What is 105,135,300 in other base number systems?
- How is 105,135,300 spelled out in other languages or countries?
- How is 105,135,300 formatted in other languages or countries?
- How is 105,135,300 formatted as currency in different languages or countries?
- What are the different hash algorithm outputs for 105,135,300?