Math Tutor Explains: What are the Factors of 1490?

As your math tutor, I’m here to guide you through the different types of factors of 1490. Understanding factors is key to mastering multiplication, division, and prime numbers. Here’s a breakdown:

• Factors of 1490: 1, 2, 5, 10, 149, 298, 745, 1490

• Sum of Factors of 1490: 2700

• Negative Factors of 1490: -1, -2, -5, -10, -149, -298, -745, -1490

• Prime Factors of 1490: 2, 5, 149

• Prime Factorization of 1490: 2^1 × 5^1 × 149^1

There are two main ways a math tutor would explain how to find the factors of 1490: 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 1490 step by step!

Factor pairs of 1490 are any two numbers that, when multiplied together, equal 1490. The question to ask is “what two numbers multiplied together equal 1490?” Every factor can be paired with another factor, and multiplying the two will result in 1490.

To find the factor pairs of 1490, follow these steps:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 1490. 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 1490 by the smallest prime factor, in this case, 2:

1490 ÷ 2 = 745

2 and 745 will make a new factor pair.

Step 3:

Repeat Steps 1 and 2, using 745 as the new focus. Find the smallest prime factor that isn’t 1, and divide 745 by that number. In this case, 5 is the new smallest prime factor:

745 ÷ 5 = 149

Remember that this new factor pair is only for the factors of 745, not 1490. So, to finish the factor pair for 1490, you’d multiply 2 and 5 before pairing with 149:

2 x 5 = 10

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 1490:

(1, 1490), (2, 745), (5, 298), (10, 149)

So, to list all the factors of 1490: 1, 2, 5, 10, 149, 298, 745, 1490

The negative factors of 1490 would be: -1, -2, -5, -10, -149, -298, -745, -1490

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 1490, we break it down step by step until only prime factors remain. Then, we express 1490 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 1490 only has a few differences from the above method of finding the factors of 1490. 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 1490:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 1490. 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 1490 by the smallest prime factor, in this case, 2

1490 ÷ 2 = 745

2 becomes the first number in our prime factorization.

Step 3:

Repeat Steps 1 and 2, using 745 as the new focus. Find the smallest prime factor that isn’t 1, and divide 745 by that number. The smallest prime factor you pick for 745 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 1490 are: 2, 5, 149

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

Factors of 56 - The factors of 56 are 1, 2, 4, 7, 8, 14, 28, 56

Factors of 117 - The factors of 117 are 1, 3, 9, 13, 39, 117

Factors of 98 - The factors of 98 are 1, 2, 7, 14, 49, 98

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