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Factors of 2490: As Taught by a Math Tutor
Methods
What are the Factors of 2490?
As your math tutor, I’m here to guide you through the different types of factors of 2490. Understanding factors is key to mastering multiplication, division, and prime numbers. Here’s a breakdown:
• Factors of 2490: 1, 2, 3, 5, 6, 10, 15, 30, 83, 166, 249, 415, 498, 830, 1245, 2490
• Sum of Factors of 2490: 6048
• Negative Factors of 2490: -1, -2, -3, -5, -6, -10, -15, -30, -83, -166, -249, -415, -498, -830, -1245, -2490
• Prime Factors of 2490: 2, 3, 5, 83
• Prime Factorization of 2490: 2^1 × 3^1 × 5^1 × 83^1
There are two main ways a math tutor would explain how to find the factors of 2490: using factor pairs and prime factorization. Let’s explore both!
The Factor Pairs of 2490
As your math tutor, I’m here to help you break down factor pairs of 2490 step by step!
Factor pairs of 2490 are any two numbers that, when multiplied together, equal 2490. The question to ask is “what two numbers multiplied together equal 2490?” Every factor can be paired with another factor, and multiplying the two will result in 2490.
To find the factor pairs of 2490, follow these steps:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 2490. 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 2.
Step 2:
Divide 2490 by the smallest prime factor, in this case, 2:
2490 ÷ 2 = 1245
2 and 1245 will make a new factor pair.
Step 3:
Repeat Steps 1 and 2, using 1245 as the new focus. Find the smallest prime factor that isn’t 1, and divide 1245 by that number. In this case, 3 is the new smallest prime factor:
1245 ÷ 3 = 415
Remember that this new factor pair is only for the factors of 1245, not 2490. So, to finish the factor pair for 2490, you’d multiply 2 and 3 before pairing with 415:
2 x 3 = 6
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 2490:
(1, 2490), (2, 1245), (3, 830), (5, 498), (6, 415), (10, 249), (15, 166), (30, 83)
So, to list all the factors of 2490: 1, 2, 3, 5, 6, 10, 15, 30, 83, 166, 249, 415, 498, 830, 1245, 2490
The negative factors of 2490 would be: -1, -2, -3, -5, -6, -10, -15, -30, -83, -166, -249, -415, -498, -830, -1245, -2490
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 2490
To find the prime factorization of 2490, we break it down step by step until only prime factors remain. Then, we express 2490 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 2490 only has a few differences from the above method of finding the factors of 2490. 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 2490:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 2490. 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 2.
Step 2:
Divide 2490 by the smallest prime factor, in this case, 2
2490 ÷ 2 = 1245
2 becomes the first number in our prime factorization.
Step 3:
Repeat Steps 1 and 2, using 1245 as the new focus. Find the smallest prime factor that isn’t 1, and divide 1245 by that number. The smallest prime factor you pick for 1245 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 2490 are: 2, 3, 5, 83
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 144 - The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
Factors of 70 - The factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70
Factors of 9 - The factors of 9 are 1, 3, 9
Factors of 90 - The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
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