Factors of 441—with division and prime factorization

Factors of 441

Factors of 441

Factors of 441 are the integers that can be equally divided by 441.

The factors with a negative sign of 441 are negative factors. Do you know that 441 is the sum of the cubes of the first six natural numbers, which is also the square of 21? We will explore the factors of 441 as well as its prime factors, as well as its factors in pairs, in this chapter.

Factors of 441

Factors of 441: 1, 3, 7, 9, 21, 49, 63, 147 and 441.

Negative Factors of 441: -1, -3, -7, -9, -21, -49, -63, -147 and -441.

Prime Factorization of 441: 3 × 3 × 7 × 7

What are Factors of 441?

Factors of 441 are all the numbers that multiply to give 441 as their product.

Factors of 441

What are Factors of -441?

When we multiply two numbers, and we get -441 as a product, that numbers are the factors of -441. 

Here is the explanation:

-1 × 441 = -441

 1 × -441 = -441

 -3 × 147 = -441

 3 × -147 = -441

 -7 × 63 = -441

 7 × -63 = -441

 -9 × 49 = -441

 9 × -49 = -441

 -21 × 21 = -441 

 21 × -21 = -441

 -49 × 9 = -441

  49 × -9 = -441

 -63 × 7 = -441

 63 × -7 = -441

 -147 × 3 = -441

 147 × -3 = -441

 -441 × 1 = -441

 441 × -1 = -441

We can get -441 by having (-1, 441), (-3, 147), (-7, 63), (-9, 49), (-21, 21), (-49, 9), (-63, 7), (-147, 3), and (-441, 1) as a pair of factors. Similarly, we can also get -441 by having(1, -441), (3, -147), (7, -63), (9, -49), (21, -21), (49, -9), (63, -7), (147, -3), and (441, -1) as a pair of factors.

 

How to Calculate the Factors of 441?

Here are the steps to calculating 35 factors:

Step 1:

Determine the number to be multiplied. The factoring number is 441.

Step 2:

Calculate the product of two numbers.

Step 3:

441 = 3 × 147, 441 = 7 × 63, 441 = 9 × 49 and 441= 21 × 21.

Therefore, the factors of 441 are 1, 3, 7, 9, 21, 49, 63, 147, and 441. Using illustrations and interactive examples, explore the factors of 441:

More Factors:

  • Factors of 37: The factors of 37 are 1 and 37.
  • Factors of 15: The factors of 15 are 1, 3, 5, and 15.
  • Factors of 45: The factors of 45 are 1, 3, 5, 9, 15, and 45.
  • Factors of 40: The factors of 40 are 1, 2, 4, 5, 8, 10, 20 and 40
  • Factors of 25: The factors of 25 are 1, 5 and 25

Factors of 441 by Prime Factorization

You can find the prime factorization factors of 35 by following these steps:

Step 1:

Determine the pair of factors which, when multiplied, give 441

    Factoring 441 can be done by multiplying 21 and 21.

Step 2:

Because 21 isn’t a prime number, 3×7 is factorable.

    Since 3 and 7 are both prime numbers, they cannot be factored further.

Step 3: T

herefore, 441 can be written as 441 = 21 × 21 = 3 × 7 × 3 × 7

Thus, 441 = 32 × 72 is the prime factorization of 441.

Factors of 441 by prime factorization

Factors of 441 in Pairs

The pair factors of the number 441 are two whole numbers that multiply each other. There could be positive or negative pair factors, but not fractions or decimals.

  • Positive factors of 441:(1, 441), (3, 147), (7, 63), (9, 49), (21, 21), (49, 9), (63, 7), (147, 3), (441, 1)
  • Negative factors of 441: (- 1, -441), (-3, -147 ), (-7, -63), (-9, -49), (-21, -21), (-49, -9), (-63, -7), (-147, -3), (-441, -1)

Tips and Tricks:

A number with a factor of 1 is the smallest. Therefore, it is a factor of 441.

Because all the digits in 441 add up to 9, 3 is a factor of 441 as well. Hence, 3 is one of its factors.

21 is a factor of 441 since it is divisible by 3 and 7.

Challenging Questions

  • John has $441. He has to distribute it among his 7 friends. If 5 of his friends get an equal amount of money and the rest 2 get the half of the amount which 5 others got. How much money will be left with John?
  • David has to travel from Town A to Town B. The distance between both towns is 441 miles. He drives at an average speed of 49 mph. He takes 10 pitstops of 20 minutes each. How long will he take to reach Town B?

Solved Examples

1. Example 1: Clarke’s school has 441 students. If there are 21 classrooms in the entire school. Help him calculate how many students can sit in each classroom?
Solution:
Clarke’s school has 441 students. There are 21 classrooms in the entire school.
To calculate the number of students in each classroom Clarke has to divide 441 by 21, (441 ÷ 21 = 21 ). He found that 21 students can sit in each classroom.

2. Example 2: Williamson went to a cinema hall having 441 chairs. If there were 9 rows in the hall, help Williamson calculate how many seats are there in each row?
Solution:
There were 441 chairs in the cinema hall. Williamson saw there were 9 rows in the hall.
To calculate the number of seats in each row he will divide 441 by 9 as given below. (441 ÷ 9 = 49 ). There will be 49 seats in each row.

FAQs 

What are the Factors of 441?

Factors of 441 = 1, 3, 7, 9, 21, 49, 63, 147, and 441.

Is 441 a Perfect Square?

By finding the prime factorization of 441, we can express it as 21 × 21. It is therefore a perfect square.

What is the Prime Factorization of 441 using Exponents?

Prime factorization of 441 by exponents is given by 441 = 32 × 72

What are the Common Factors of 441 and 567?

Factors of 441 = 1, 3, 7, 9, 21, 49, 63, 147, and 441.

Factors of 567 = 1, 3, 7, 9, 21, 27, 63, 81, 189, and 567.

Thus, the common factors of 441 and 567 are 1, 3, 7, 9, 21, and 63.

What are the Prime Factors of 441?

There are two distinct prime factors in 441: 3 and 7.

What is the Product of the Prime Factors of 441?

The number 441 is equal to 3 × 3 × 7 × 7. 3 and 7 are distinct prime factors. Hence, the product is 21.

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