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Factors of 6300: As Taught by a Math Tutor
Methods
What are the Factors of 6300?
As your math tutor, I’m here to guide you through the different types of factors of 6300. Understanding factors is key to mastering multiplication, division, and prime numbers. Here’s a breakdown:
• Factors of 6300: 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 25, 28, 30, 35, 36, 42, 45, 50, 60, 63, 70, 75, 84, 90, 100, 105, 126, 140, 150, 175, 180, 210, 225, 252, 300, 315, 350, 420, 450, 525, 630, 700, 900, 1050, 1260, 1575, 2100, 3150, 6300
• Sum of Factors of 6300: 22568
• Negative Factors of 6300: -1, -2, -3, -4, -5, -6, -7, -9, -10, -12, -14, -15, -18, -20, -21, -25, -28, -30, -35, -36, -42, -45, -50, -60, -63, -70, -75, -84, -90, -100, -105, -126, -140, -150, -175, -180, -210, -225, -252, -300, -315, -350, -420, -450, -525, -630, -700, -900, -1050, -1260, -1575, -2100, -3150, -6300
• Prime Factors of 6300: 2, 3, 5, 7
• Prime Factorization of 6300: 2^2 × 3^2 × 5^2 × 7^1
There are two main ways a math tutor would explain how to find the factors of 6300: using factor pairs and prime factorization. Let’s explore both!
The Factor Pairs of 6300
As your math tutor, I’m here to help you break down factor pairs of 6300 step by step!
Factor pairs of 6300 are any two numbers that, when multiplied together, equal 6300. The question to ask is “what two numbers multiplied together equal 6300?” Every factor can be paired with another factor, and multiplying the two will result in 6300.
To find the factor pairs of 6300, follow these steps:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 6300. 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 6300 by the smallest prime factor, in this case, 2:
6300 ÷ 2 = 3150
2 and 3150 will make a new factor pair.
Step 3:
Repeat Steps 1 and 2, using 3150 as the new focus. Find the smallest prime factor that isn’t 1, and divide 3150 by that number. In this case, 2 is the new smallest prime factor:
3150 ÷ 2 = 1575
Remember that this new factor pair is only for the factors of 3150, not 6300. So, to finish the factor pair for 6300, you’d multiply 2 and 2 before pairing with 1575:
2 x 2 = 4
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 6300:
(1, 6300), (2, 3150), (3, 2100), (4, 1575), (5, 1260), (6, 1050), (7, 900), (9, 700), (10, 630), (12, 525), (14, 450), (15, 420), (18, 350), (20, 315), (21, 300), (25, 252), (28, 225), (30, 210), (35, 180), (36, 175), (42, 150), (45, 140), (50, 126), (60, 105), (63, 100), (70, 90), (75, 84)
So, to list all the factors of 6300: 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 25, 28, 30, 35, 36, 42, 45, 50, 60, 63, 70, 75, 84, 90, 100, 105, 126, 140, 150, 175, 180, 210, 225, 252, 300, 315, 350, 420, 450, 525, 630, 700, 900, 1050, 1260, 1575, 2100, 3150, 6300
The negative factors of 6300 would be: -1, -2, -3, -4, -5, -6, -7, -9, -10, -12, -14, -15, -18, -20, -21, -25, -28, -30, -35, -36, -42, -45, -50, -60, -63, -70, -75, -84, -90, -100, -105, -126, -140, -150, -175, -180, -210, -225, -252, -300, -315, -350, -420, -450, -525, -630, -700, -900, -1050, -1260, -1575, -2100, -3150, -6300
Prime Factorization of 6300
To find the prime factorization of 6300, we break it down step by step until only prime factors remain. Then, we express 6300 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 6300 only has a few differences from the above method of finding the factors of 6300. 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 6300:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 6300. 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 6300 by the smallest prime factor, in this case, 2
6300 ÷ 2 = 3150
2 becomes the first number in our prime factorization.
Step 3:
Repeat Steps 1 and 2, using 3150 as the new focus. Find the smallest prime factor that isn’t 1, and divide 3150 by that number. The smallest prime factor you pick for 3150 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 6300 are: 2, 3, 5, 7
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 87 - The factors of 87 are 1, 3, 29, 87
Factors of 146 - The factors of 146 are 1, 2, 73, 146
Factors of 20 - The factors of 20 are 1, 2, 4, 5, 10, 20
Factors of 24 - The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24
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