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Factors of 1695: As Taught by a Math Tutor
Methods
What are the Factors of 1695?
As your math tutor, I’m here to guide you through the different types of factors of 1695. Understanding factors is key to mastering multiplication, division, and prime numbers. Here’s a breakdown:
• Factors of 1695: 1, 3, 5, 15, 113, 339, 565, 1695
• Sum of Factors of 1695: 2736
• Negative Factors of 1695: -1, -3, -5, -15, -113, -339, -565, -1695
• Prime Factors of 1695: 3, 5, 113
• Prime Factorization of 1695: 3^1 × 5^1 × 113^1
There are two main ways a math tutor would explain how to find the factors of 1695: using factor pairs and prime factorization. Let’s explore both!
The Factor Pairs of 1695
As your math tutor, I’m here to help you break down factor pairs of 1695 step by step!
Factor pairs of 1695 are any two numbers that, when multiplied together, equal 1695. The question to ask is “what two numbers multiplied together equal 1695?” Every factor can be paired with another factor, and multiplying the two will result in 1695.
To find the factor pairs of 1695, follow these steps:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 1695. For reference, the first prime numbers to check are 2, 3, 5, 7, 11, and 13. In this case, the smallest factor that’s a prime number larger than 1 is 3.
Step 2:
Divide 1695 by the smallest prime factor, in this case, 3:
1695 ÷ 3 = 565
3 and 565 will make a new factor pair.
Step 3:
Repeat Steps 1 and 2, using 565 as the new focus. Find the smallest prime factor that isn’t 1, and divide 565 by that number. In this case, 5 is the new smallest prime factor:
565 ÷ 5 = 113
Remember that this new factor pair is only for the factors of 565, not 1695. So, to finish the factor pair for 1695, you’d multiply 3 and 5 before pairing with 113:
3 x 5 = 15
Step 4:
Repeat this process until there are no longer any prime factors larger than one to divide by. At the end, you should have the full list of factor pairs.
Here are all the factor pairs for 1695:
(1, 1695), (3, 565), (5, 339), (15, 113)
So, to list all the factors of 1695: 1, 3, 5, 15, 113, 339, 565, 1695
The negative factors of 1695 would be: -1, -3, -5, -15, -113, -339, -565, -1695
Now you’ve got it! A math tutor would always encourage you to practice with different numbers to reinforce your understanding of factor pairs. Try another one!
Prime Factorization of 1695
To find the prime factorization of 1695, we break it down step by step until only prime factors remain. Then, we express 1695 as a product of these prime factors multiplied together. Let’s go through the process and simplify it like a math tutor would!
The process of finding the prime factorization of 1695 only has a few differences from the above method of finding the factors of 1695. Instead of ensuring we find the right factor pairs, we continue to factor each step until we are left with only the list of smallest prime factors greater than 1.
Here are the steps for finding the prime factorization of 1695:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 1695. For reference, the first prime numbers to check are 2, 3, 5, 7, 11, and 13. In this case, the smallest factor that’s a prime number larger than 1 is 3.
Step 2:
Divide 1695 by the smallest prime factor, in this case, 3
1695 ÷ 3 = 565
3 becomes the first number in our prime factorization.
Step 3:
Repeat Steps 1 and 2, using 565 as the new focus. Find the smallest prime factor that isn’t 1, and divide 565 by that number. The smallest prime factor you pick for 565 will then be the next prime factor. If you keep repeating this process, there will be a point where there will be no more prime factors left, which leaves you with the prime factors for prime factorization.
So, the unique prime factors of 1695 are: 3, 5, 113
Math Tutor Suggests: Find the Factors of Other Numbers
Practice your factoring skills by exploring how to factor other numbers, like the ones below:
Factors of 61 - The factors of 61 are 1, 61
Factors of 75 - The factors of 75 are 1, 3, 5, 15, 25, 75
Factors of 118 - The factors of 118 are 1, 2, 59, 118
Factors of 116 - The factors of 116 are 1, 2, 4, 29, 58, 116
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