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Factors of 441

Factors of 441 are the list of integers that can be evenly divided into 441. Negative factors of 441 are just factors with a negative sign. Did you know that the sum of cubes of the first six natural numbers is 441, which is also the square of 21? In this chapter, we will explore the factors of 441 along with its prime factors, and its factors in pairs.

  • 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
1. What are Factors of 441?
2. How to Calculate Factors of 441?
3. Factors of 441 by Prime Factorization
4. Factors of 441 in Pairs
5. Tips And Tricks
6. Challenging Questions
7. FAQs on Factors of 441

What are Factors of 441?

Factors of 441 are all the numbers that are multiplied to get 441 as their product.

factors of 441

How to Calculate the Factors of 441?

Let's learn how to calculate factors of 35:

  • Step 1: Write down the number to be factored in. The number to be factored in is 441
  • Step 2: Find the two numbers whose product gives 441.
  • Step 3: 441 = 3 × 147 , 441 = 7 × 63, 441 = 9 × 49 and 441= 21 × 21.

Thus we obtain the factors of 441 as 1, 3, 7, 9, 21, 49, 63, 147, and 441. Explore factors using illustrations and interactive examples:

Factors of 441 by Prime Factorization

Factors of 35 by prime factorization are given by using the following steps:

  • Step 1: Write the pair of factors, which on multiplication gives 441
    • 441 can be factored as a product of 21 and 21
  • Step 2: 21 is not a prime number and can be factored in 3 × 7.
    • 3 and 7 are both prime numbers hence they cannot be factored further.
  • Step 3: As per the criterion,441 can thereby be written as 441 = 21 × 21 = 3 × 7 × 3 × 7

Hence, the prime factors of 441 can be written as 441 = 32 × 72

Factors of 441 by Prime Factorization

Factors of 441 in Pairs

Pair factors of the number 441 are the two whole numbers that multiply to get the original number. Pair factors could be either positive or negative but not a fraction or a decimal number.

  • 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:

  • 1 is the smallest factor of every number. Hence, it is a factor of 441
  • 3 is a factor of 441 because the sum of all the digits of 441 is 9 which is divisible by 3. Hence, 3 is one of its factors.
  • 441 is divisible by 3 and 7, hence 21 is one of its factors.

Challenging Questions

  • Christian 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 Christian?
  • John 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?
 

Factors of 441 Solved Examples

  1. Example 1:Jessie's school has 441 students. If there are 21 classrooms in the entire school. Help her calculate how many students can sit in each classroom?

    Solution:

    Jessie's school has 441 students. There are 21 classrooms in the entire school.

    To calculate the number of students in each classroom Jessie has to divide 441 by 21, (441 ÷ 21 = 21 ). She found that 21 students can sit in each classroom.

  2. Example 2: Ashton went to a cinema hall having 441 chairs. If there were 9 rows in the hall, help Ashton calculate how many seats are there in each row?

    Solution:

    There were 441 chairs in the cinema hall. Ashton 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.

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FAQs on Factors of 441

What are the Factors of 441?

The factors of 441 are 1, 3, 7, 9, 21, 49, 63, 147, and 441.

Is 441 a Perfect Square?

Finding the prime factorization of 441, we can express as 21 × 21. So it is a perfect square.

What is the Prime Factorization of 441 using Exponents?

The prime factorization of 441 using exponents is given by 441 = 32 × 72

What are the Common Factors of 441 and 567?

The factors of 441 are 1, 3, 7, 9, 21, 49, 63, 147, and 441 and the factors of 567 are 1, 3, 7, 9, 21, 27, 63, 81, 189 and 567.

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

What are the Prime Factors of 441?

The distinct prime factors of 441 are 3 and 7.

What is the Product of the Prime Factors of 441?

441 = 3 × 3 × 7 × 7. The distinct prime factors are 3 and 7. Their product is 21.

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