Math Tutor Explains: What are the Factors of 1410?

As your math tutor, I’m here to guide you through the different types of factors of 1410. Understanding factors is key to mastering multiplication, division, and prime numbers. Here’s a breakdown:

• Factors of 1410: 1, 2, 3, 5, 6, 10, 15, 30, 47, 94, 141, 235, 282, 470, 705, 1410

• Sum of Factors of 1410: 3456

• Negative Factors of 1410: -1, -2, -3, -5, -6, -10, -15, -30, -47, -94, -141, -235, -282, -470, -705, -1410

• Prime Factors of 1410: 2, 3, 5, 47

• Prime Factorization of 1410: 2^1 × 3^1 × 5^1 × 47^1

There are two main ways a math tutor would explain how to find the factors of 1410: using factor pairs and prime factorization. Let’s explore both!

As your math tutor, I’m here to help you break down factor pairs of 1410 step by step!

Factor pairs of 1410 are any two numbers that, when multiplied together, equal 1410. The question to ask is “what two numbers multiplied together equal 1410?” Every factor can be paired with another factor, and multiplying the two will result in 1410.

To find the factor pairs of 1410, follow these steps:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 1410. 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 1410 by the smallest prime factor, in this case, 2:

1410 ÷ 2 = 705

2 and 705 will make a new factor pair.

Step 3:

Repeat Steps 1 and 2, using 705 as the new focus. Find the smallest prime factor that isn’t 1, and divide 705 by that number. In this case, 3 is the new smallest prime factor:

705 ÷ 3 = 235

Remember that this new factor pair is only for the factors of 705, not 1410. So, to finish the factor pair for 1410, you’d multiply 2 and 3 before pairing with 235:

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 1410:

(1, 1410), (2, 705), (3, 470), (5, 282), (6, 235), (10, 141), (15, 94), (30, 47)

So, to list all the factors of 1410: 1, 2, 3, 5, 6, 10, 15, 30, 47, 94, 141, 235, 282, 470, 705, 1410

The negative factors of 1410 would be: -1, -2, -3, -5, -6, -10, -15, -30, -47, -94, -141, -235, -282, -470, -705, -1410

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!

To find the prime factorization of 1410, we break it down step by step until only prime factors remain. Then, we express 1410 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 1410 only has a few differences from the above method of finding the factors of 1410. 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 1410:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 1410. 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 1410 by the smallest prime factor, in this case, 2

1410 ÷ 2 = 705

2 becomes the first number in our prime factorization.

Step 3:

Repeat Steps 1 and 2, using 705 as the new focus. Find the smallest prime factor that isn’t 1, and divide 705 by that number. The smallest prime factor you pick for 705 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 1410 are: 2, 3, 5, 47

Practice your factoring skills by exploring how to factor other numbers, like the ones below:

Factors of 8 - The factors of 8 are 1, 2, 4, 8

Factors of 14 - The factors of 14 are 1, 2, 7, 14

Factors of 109 - The factors of 109 are 1, 109

Factors of 100 - The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100