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Factors of 1407: As Taught by a Math Tutor
Methods
What are the Factors of 1407?
As your math tutor, I’m here to guide you through the different types of factors of 1407. Understanding factors is key to mastering multiplication, division, and prime numbers. Here’s a breakdown:
• Factors of 1407: 1, 3, 7, 21, 67, 201, 469, 1407
• Sum of Factors of 1407: 2176
• Negative Factors of 1407: -1, -3, -7, -21, -67, -201, -469, -1407
• Prime Factors of 1407: 3, 7, 67
• Prime Factorization of 1407: 3^1 × 7^1 × 67^1
There are two main ways a math tutor would explain how to find the factors of 1407: using factor pairs and prime factorization. Let’s explore both!
The Factor Pairs of 1407
As your math tutor, I’m here to help you break down factor pairs of 1407 step by step!
Factor pairs of 1407 are any two numbers that, when multiplied together, equal 1407. The question to ask is “what two numbers multiplied together equal 1407?” Every factor can be paired with another factor, and multiplying the two will result in 1407.
To find the factor pairs of 1407, follow these steps:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 1407. 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 1407 by the smallest prime factor, in this case, 3:
1407 ÷ 3 = 469
3 and 469 will make a new factor pair.
Step 3:
Repeat Steps 1 and 2, using 469 as the new focus. Find the smallest prime factor that isn’t 1, and divide 469 by that number. In this case, 7 is the new smallest prime factor:
469 ÷ 7 = 67
Remember that this new factor pair is only for the factors of 469, not 1407. So, to finish the factor pair for 1407, you’d multiply 3 and 7 before pairing with 67:
3 x 7 = 21
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 1407:
(1, 1407), (3, 469), (7, 201), (21, 67)
So, to list all the factors of 1407: 1, 3, 7, 21, 67, 201, 469, 1407
The negative factors of 1407 would be: -1, -3, -7, -21, -67, -201, -469, -1407
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 1407
To find the prime factorization of 1407, we break it down step by step until only prime factors remain. Then, we express 1407 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 1407 only has a few differences from the above method of finding the factors of 1407. 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 1407:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 1407. 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 1407 by the smallest prime factor, in this case, 3
1407 ÷ 3 = 469
3 becomes the first number in our prime factorization.
Step 3:
Repeat Steps 1 and 2, using 469 as the new focus. Find the smallest prime factor that isn’t 1, and divide 469 by that number. The smallest prime factor you pick for 469 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 1407 are: 3, 7, 67
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 76 - The factors of 76 are 1, 2, 4, 19, 38, 76
Factors of 63 - The factors of 63 are 1, 3, 7, 9, 21, 63
Factors of 54 - The factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54
Factors of 26 - The factors of 26 are 1, 2, 13, 26
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