Factors

# Factors of 126 | Prime Factorization of 126 | Factor Tree of 126

Written by Prerit Jain

Updated on: 21 Jun 2023

## Factors of 126

Calculate Factors of

The Factors are

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## What are the factors of 126

The factors of 126 are the numbers that can divide 126 evenly, with no remainder. To find the factors of 126, we can start by dividing them by 2 to see if it is even. 126 divided by 2 is 63, which is an odd number, so 2 is not a factor of 126.

We can continue to divide by 2 to find more factors, or we can start dividing by other numbers. One way to find all of the factors of 126 is to make a list of all of the numbers that divide into 126 evenly. We can start with the number 1 and work our way up.

The factors of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, and 126.

We can check that these numbers are all divided into 126 evenly by dividing 126 by each one. For example, 126 divided by 2 is 63, and 126 divided by 3 is 42. All of these numbers divide into 126 evenly, so they are all factors of 126.

## How to Find Factors of 126

The following are the methods through which you can find the factors of 126:

• Factors of 126 using the Multiplication Method
• Factors of 126 using the Division Method
• Prime Factorization of 126
• Factor tree of 126

## Factors of 126 Using the Multiplication Method

The multiplication method is a way to find the factors of a number by multiplying pairs of numbers together. To use this method to find the factors of 126, we can list all of the numbers that can be multiplied together to get 126. We can start with the number 1 and work our way up.

Here is the list of factors of 126 using the multiplication method:

1 x 126 = 126

2 x 63 = 126

3 x 42 = 126

6 x 21 = 126

9 x 14 = 126

18 x 7 = 126

In each case, we are multiplying two numbers together to get 126. For example, when we multiply 2 x 63, we are adding 2 to itself 63 times to get 126. When we multiply 3 x 42, we are adding 3 to itself 42 times to get 126.

To understand this method, it can be helpful to think about what we are doing when we multiply numbers together. When we multiply two numbers, we are adding one number to itself a certain number of times. For example, when we multiply 2 x 3, we are adding 2 to itself 3 times: 2 + 2 + 2 = 6.

## Factors of 126 Using the Division Method

The division method is a way to find the factors of a number by dividing the number by different numbers and seeing if there is a remainder. To use this method to find the factors of 126, we can divide 126 by each number to see if there is a remainder. If there is no remainder, then the number is a factor of 126.

Here is the list of all of the factors of 126 using the division method:

126 ÷ 1 = 126 (no remainder)

126 ÷ 2 = 63 (no remainder)

126 ÷ 3 = 42 (no remainder)

126 ÷ 6 = 21 (no remainder)

126 ÷ 9 = 14 (no remainder)

126 ÷ 18 = 7 (no remainder)

126 ÷ 42 = 3 (no remainder)

126 ÷ 63 = 2 (no remainder)

126 ÷ 126 = 1 (no remainder)

Since there is no remainder when we divide 126 by any of these numbers, they are all factors of 126. This means that these are all of the numbers that can be divided into 126 evenly, with no remainder.

## Prime Factorization of 126

Calculate Prime Factors of

The Prime Factors of 126 =

2 x

3 x

3 x

7

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The prime factorization of a number is a way to express that number as a product of prime numbers. A prime number is a number that is only divisible by 1 and itself, such as 2, 3, 5, and 7. To find the prime factorization of a number, we can divide it by the smallest possible prime number and see if it is a factor. If it is a factor, we can divide the result by the same prime number to see if it is a factor. We can repeat this process with other prime numbers until we have found all of the prime factors.

For example, to find the prime factorization of 126, we can start by dividing it by 2 to see if it is a factor. 126 divided by 2 is 63, which is an odd number, so 2 is not a factor of 126. We can divide 126 by 3 to see if it is a factor. 126 divided by 3 is 42 with a remainder of 0, so 3 is a factor of 126. We can repeat this process with other prime numbers until we have found all of the prime factors.

The prime factorization of 126 is 2 x 3 x 3 x 7.

Because these are the prime numbers that can be multiplied together to get 126. We can check that this is the prime factorization of 126 by multiplying the prime numbers together to get 126: 2 x 3 x 3 x 7 = 126

## Factor tree of 126

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A factor tree is a way to represent the prime factorization of a number in a visual form. It is a tree-like diagram that shows how the original number can be broken down into smaller factors until only prime numbers are left.

To create a factor tree for 126, we start with the original number and look for a factor. In this case, 126 is divisible by 2, but 2 is not a prime number, so we continue to divide by other numbers. We can divide 126 by 3, which is a prime number, so we write 3 as one of the branches of the tree. We then divide 126 by 3 to get the next number on the tree, which is 42. We can divide 42 by 2, but 2 is not a prime number, so we continue to divide by other numbers. We can divide 42 by 3 to get 14, which is not divisible by any more prime numbers, so we stop here.

Here is a factor tree for 126:

The prime factorization of 126 is the list of prime numbers that can be multiplied together to get 126. In this case, the prime factorization of 126 is 2 x 3 x 3 x 7, because these are the prime numbers that can be multiplied together to get 126.

## Factor Pairs of 126

Calculate Pair Factors of

1 x 126=126

2 x 63=126

3 x 42=126

6 x 21=126

7 x 18=126

9 x 14=126

14 x 9=126

18 x 7=126

21 x 6=126

42 x 3=126

63 x 2=126

So Pair Factors of 126 are

(1,126)

(2,63)

(3,42)

(6,21)

(7,18)

(9,14)

(14,9)

(18,7)

(21,6)

(42,3)

(63,2)

https://wiingy.com/learn/math/factors-of-126/

The factor pairs of a number are all the pairs of numbers that can be multiplied together to get the original number. To find the factor pairs of a number, we can start by listing all of the factors of the number.

To find the factor pairs of 126, we can start by making a list of all of the factors of 126: 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, and 126.

We can then pair these factors together to get all of the factor pairs of 126. Here is the list of factor pairs of 126:

(1, 126), (2, 63), (3, 42), (6, 21), (9, 14) and (18, 7).

## Factors of 126 – Quick Recap

• Factors of 126:  1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126.
• Negative Factors of 126:   -1, -2, -3, -6, -7, -9, -14, -18, -21, -42, -63, -126.
• Prime Factors of 126:2, 3, and 7
• Prime Factorization of 126:  2, 3, and 7.

Also Check: Multiples, Square Root, and LCM

## Solved Examples of Factor of 126

Q.1: Jamie needs to purchase supplies for a class project; if there are 126 students in the class and he needs to buy 4 supplies per student, how many total supplies does he need to purchase?
Solution: Jamie needs to purchase 504 supplies in this case.

Q.2: Matt has 1260 pictures he wants to divide among 126 people, how many pictures should each person receive?
Solution: Each person should receive 10 pictures in this case.

Q.3: If Matthew has 126 stamps that need to be divided between 7 people, how many stamps should each person get?
Solution:
Each person should get 18 stamps from Matthew’s supply.

Q.4: Kate is baking cookies; she needs 1260 grams of chocolate chips and wants to divide them into 10 parts, how much chocolate will each part contain?
Solution: Each part will contain 10 grams of chocolate chips in this case.

Q.5: Tom works at a book store and they have received a shipment of 126 books, if they plan to sell them individually, how much money can they make with one book?
Solution: In this case, they can make \$1 with every sale of one book.

Q.6: What is the greatest common factor between 1262 and 1848?
Solution:
The greatest common factor between 1262 and 1848 is 2.

Q.7: How many students can each attend the lecture if there are 1260 chairs available and 21 classes?
Solution:
Each student can attend 60 chairs for attendance in this case.

Q.8: If there are 125 customers attending an event at the museum, but 3 out of every 5 customers receive a special discount on tickets, what percentage of customers will get the discount?
Solution:
Out of every 5 customers, 3 receive the discount. So the ratio of customers receiving the discount to the total number of customers is 3/5. To find the percentage, we multiply this ratio by 100: (3/5) * 100 = 60%.

## Frequently Asked Questions on Factors of 126

### What are the factors of 126?

The factors of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, and 126.

### What is the greatest common factor (GCF) for 126 and 124?

The factors of 126 are: 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, and 126. The factors of 124 are: 1, 2, 4, 31, 62, and 124.
The common factors of 126 and 124 are: 1 and 2.
Therefore, the greatest common factor (GCF) of 126 and 124 is 2.

### What are the prime factors of 126?

The prime factors of 126 are 2 x 3 x 3 x 7.

### How many divisors does the number 126 have?

The number 126 has 12 divisors – 1, 2, 3, 6, 7, 9, 14, 18, 21, 42,63, and 126.

### Can you use division to find out if a number is a factor of another number?

Yes – if a division operation between two numbers yields no remainder then that means the second number was a factor of the first one. For example, to know if 6 is a factor of126, we can divide it and check that the result has no remainder – which indeed it doesn’t(126 divided by 6 equals 21).  Thus we know 6 is one of the factors of 126.

### Are there any perfect squares between 121 and 127?

Yes – 121 = 11 x 11 .

### What is the HCF or GCD for 124 and 128?

The factors of 124 are 1, 2, 4, 31, 62, and 124. The factors of 128 are 1, 2, 4, 8, 16, 32, 64, and 128.
The common factors of 124 and 128 are 1, 2, 4.
Therefore, the highest common factor (HCF) or greatest common divisor (GCD) of 124 and 128 is 4.

### If someone needed to purchase 1262 books from a store, how much would they need to spend if each book costs \$6?

1262 books * \$6/book = \$7572
Therefore, if each book costs \$6, someone would need to spend \$7572 to purchase 1262 books from the store.

Written by by

Prerit Jain

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