36 factors, again!

TL;DR

An explanation of how to find the number of factors a given number has and how to find a number with a specific number of factors.

Transcript

okay hopefully guess i'll have a chance to try it and i know some of you guys cannot wait so i will tell you guys what the answer is the answer to this is one thousand two hundred and sixty yes this right here is enough to have 36 factors okay and you can comment down below and share your approach with us and i'm going to share mine with you right ... Read More

Key Insights

• #️⃣ The number of factors a given number has can be found by prime factoring the number and counting the exponents.
• 🧑‍🏭 The formula to find the number of factors involves adding 1 to each exponent and multiplying the results.
• #️⃣ To find a number with a specific number of factors, factorize that number and distribute the factors evenly among primes.
• #️⃣ It is possible to find a number with the same number of factors using different combinations of primes.

Questions & Answers

Q: How do you find the number of factors a given number has?

To find the number of factors, prime factorize the number and count the exponents. The number of factors is equal to (exponent + 1) for each prime factor, and the total number of factors is the product of these values.

Q: Can you explain the example of finding the number of factors for the number 20?

For the number 20, the prime factorization is 2^2 * 5^1. Since there are 2 choices for the exponent of 2 (0 and 1), and 1 choice for the exponent of 5 (0), the number 20 has (2+1) * (1+1) = 6 factors.

Q: How can you find a number with a specific number of factors, like 36?

To find a number with 36 factors, you need to factorize 36. One way to factorize 36 is 6 * 6. This translates to a number in the form of p1^5 * p2^5. By choosing appropriate primes for p1 and p2, you can find a number with 36 factors.

Q: Can you explain the process of finding a number with 36 factors using the example given in the content?

In the example, the number with 36 factors is found by choosing p1 as 2, p2 as 5, and p3 as 3. The resulting number is 2^5 * 5^2 * 3^1, which equals 1440. However, it is noted that this may not be the smallest possible number with 36 factors, and further exploration is encouraged.

Summary & Key Takeaways

• The content discusses how to find the number of factors a given number has and provides an example using the number 20.

• It explains a formula to find the number of factors, which involves prime factoring the number and counting the exponents.

• It demonstrates how to find a number with a specific number of factors, using the example of finding a number with 36 factors.