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Factors of 2987: As Taught by a Math Tutor
Methods
What are the Factors of 2987?
As your math tutor, I’m here to guide you through the different types of factors of 2987. Understanding factors is key to mastering multiplication, division, and prime numbers. Here’s a breakdown:
• Factors of 2987: 1, 29, 103, 2987
• Sum of Factors of 2987: 3120
• Negative Factors of 2987: -1, -29, -103, -2987
• Prime Factors of 2987: 29, 103
• Prime Factorization of 2987: 29^1 × 103^1
There are two main ways a math tutor would explain how to find the factors of 2987: using factor pairs and prime factorization. Let’s explore both!
The Factor Pairs of 2987
As your math tutor, I’m here to help you break down factor pairs of 2987 step by step!
Factor pairs of 2987 are any two numbers that, when multiplied together, equal 2987. The question to ask is “what two numbers multiplied together equal 2987?” Every factor can be paired with another factor, and multiplying the two will result in 2987.
To find the factor pairs of 2987, follow these steps:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 2987. 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 29.
Step 2:
Divide 2987 by the smallest prime factor, in this case, 29:
2987 ÷ 29 = 103
29 and 103 will make a new factor pair.
Step 3:
Repeat Steps 1 and 2, using 103 as the new focus. Find the smallest prime factor that isn’t 1, and divide 103 by that number. In this case, 103 is the new smallest prime factor:
103 ÷ 103 = 1
Remember that this new factor pair is only for the factors of 103, not 2987. So, to finish the factor pair for 2987, you’d multiply 29 and 103 before pairing with 1:
29 x 103 = 2987
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 2987:
(1, 2987), (29, 103)
So, to list all the factors of 2987: 1, 29, 103, 2987
The negative factors of 2987 would be: -1, -29, -103, -2987
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 2987
To find the prime factorization of 2987, we break it down step by step until only prime factors remain. Then, we express 2987 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 2987 only has a few differences from the above method of finding the factors of 2987. 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 2987:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 2987. 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 29.
Step 2:
Divide 2987 by the smallest prime factor, in this case, 29
2987 ÷ 29 = 103
29 becomes the first number in our prime factorization.
Step 3:
Repeat Steps 1 and 2, using 103 as the new focus. Find the smallest prime factor that isn’t 1, and divide 103 by that number. The smallest prime factor you pick for 103 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 2987 are: 29, 103
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 143 - The factors of 143 are 1, 11, 13, 143
Factors of 77 - The factors of 77 are 1, 7, 11, 77
Factors of 36 - The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 101 - The factors of 101 are 1, 101
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