What are the Factors of 42 and 6?

What is the LCM and GCF of 42 and 6?

Multiples of 42: 42, 84, 126, 168, 210, 252, etc.

Multiples of 6: 6, 12, 18, 24, 30, 36, etc.

Factors of 42: 1, 2, 3, 6, 7, 14, 21, and 42.

Factors of 6: 1, 2, 3, and 6.

In summary, the answer to the question "What is the LCM and GCF of 42 and 6?" is 42 and 6.

What is the LCM and GCF of 42 and 7?

Factors are an important concept in arithmetic. Factors of 42 are simply numbers — more than two, which upon multiplication lead to the result or product of 42. In simple terms, factors are two or more numbers which upon multiplication lead to another number.  Factors are also explored in algebra. Since algebra uses variables most of the time, the factors of an algebraic term are also in the form of variables.

The example below can explain this further:

(x2 + 5x + 5) is an algebraic term with two factors (x+5) and (x+ 1)

(x+5)(x+ 1) = x2 + 5x + 5

Know the Factors of 42

Factors of 42 are simply numbers, more than two, which upon multiplication lead to the result or product of 42. Other important concepts for solving for factors are prime numbers, multiplication tables up to 20, negative and positive numbers.

Let's discover the factors of 42 through the division method. 

Starting from the smallest number, let's find the common factors 42 by division method:

Following the multiplication tables up to 20, we can easily find the factors of 42. 

The factors of 42 obtained are 42, 21, 14, 7, and 6.

In order to know more factors of 42, we can start dividing 42 with the factors that we have obtained until now. 

With the above method, we have found 3 more new factors of 42 that are 1, 2, and 3. The common factors for 42 are 6 and 7. 

Therefore the total number of factors that 42 has is 8 and they are 1, 2, 3, 6, 7, 14, 21, and 42.

Pairs of factors is another approach of finding factors of a number. The pairs of factors for 42 can be derived from the single factors that we have found above: 1, 2, 3, 6, 7, 14, 21, and 42.

Use the approach below in order to understand the methodology behind a pair of two factors:

From the calculation above, it can be inferred that there are 4 pairs of two factors for 42. They are (1, 42), (2 x 21), (3 x 14) and (6x 7). You can observe that these pairs of factors have been derived originally from the factors obtained through division. Therefore, it is highly recommended that you use the division approach when attempting questions on factors.

Just as there are pairs of two factors, there are also pairs of three and more factors for a product. This approach is used to find the smallest factors of 42. Similar to pairs of two factors, we will be using the factors derived from the division method: 1, 2, 3, 6, 7, 14, 21, and 42.

From the calculations above, we can see that there can be a pair of three factors for 42, and they are  (2, 3, 7), (1, 2, 21), (1, 3, 14), and (1, 6, 7).

Factors can also be positive and negative numbers. This means that a positive product can also be due to the multiplication of two negative factors. By simply adding the negative sign for each factor, you can get a positive product with negative factors. It can be put as follow:

Therefore the factors for 42 can also be a pair of two factors such as (-1, -42), (-2, -21), (-3, -14) and (-6, -7)

Prime Factorization of 42

The number 42 is made up of several different numbers. Let's look for 42's prime factors now.

• The first step is to divide 42 by the smallest prime factor, which is two.

42 ÷ 2 = 2

• Check to see if 21 can be split by two more times.

10.5 + 2 = 21

A factor, on the other hand, cannot be a fraction. As a result, we'll move on to the next prime number, which is three.

• Now, if we divide 21 by 3, we get

21 ÷ 3 = 7

• Divide 7 by 3 to get a fraction number once more. As a result, evaluate the next prie number, 5, as well.

Again, a fraction number, 21 5 = 4.2.

So 7 is the next prime number.

7 ÷ 7 = 1

• We've got 1 at the end, and we can't use the division approach because we know the multiple of 1 is only 1. 2 3 7 are the prime factors of 42, with 2, 3 and 7 being prime numbers.

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You have reached us maybe looking for answers to the questions like: What is the greatest common factor of 6 and 42? or what is the highest common factor (HCF) of 6 and 42?

What is the GCF of 6 and 42?

The first step to find the gcf of 6 and 42 is to list the factors of each number. The factors of 6 are 1, 2, 3 and 6. The factors of 42 are 1, 2, 3, 6, 7, 14, 21 and 42. So, the Greatest Common Factor for these numbers is 6 because it divides all them without a remainder. Read more about Common Factors below.

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The first step is to find all divisors of each number. For instance, let us find the gcf(6, 42).

In this case we have:

• The factors of 6 (all the whole numbers that can divide the number without a remainder) are 1, 2, 3 and 6;
• The factors of 42 are 1, 2, 3, 6, 7, 14, 21 and 42.

The second step is to analyze which are the common divisors. It is not difficult to see that the 'Greatest Common Factor' or 'Divisor' for 6 and 42 is 6. The GCF is the largest common positive integer that divides all the numbers (6, 42) without a remainder.

In the name greatest common divisor, the adjective "greatest" may be replaced by "highest", and the word "divisor" may be replaced by "factor", so that other names include highest common factor (hcf), greatest common measure, among others.

So, the GCF is also known as:

• Greatest common divisor (gcd);
• Highest common factor (hcf);
• Greatest common measure (gcm), or
• Highest common divisor

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