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All the factors of 50 are the numbers, which generates the results as 50 when multiplied together in pairs or the number that divides the number 50 completely without leaving any remaining values. As 50 is a composite factor, it has more than 2 factors.

To find all the factors of 50, we will consider the numbers that can divide the 50 completely without leaving any remainder. We will start dividing the number 50 with 1, then move on to 2,3 up to 25 (which is just half of the number 50). In this way, we can find the numbers that can divide the 50 completely without leaving any remainder. Accordingly, all the factors of 50 obtained with this method are 1,2,5,10, 25, and 50.

In Mathematics, prime factorization of a number 50, is the set consisting of prime numbers whose product is 50. Accordingly, the prime factorization of 50 are :

50 = 2 x 5 x 5 or 2 x 5²

Following are the steps to find the prime factorization of 50:

Step 1: Divide the number 50 with the smallest prime number i.e. 2. 50 divided by 2 gives 25.

Step 2: We can see the number 25 cannot be divided by 2 again. Hence, we will look for the next prime integer that the number 25 is divided by, which happens to be 3. Dividing 25 by 3 gives us the result 8.333, which is not a factor.

Step 3: Now, we will look for the next prime integer that the number 25 is divided by, which happens to be 5. Dividing 25 by 5, gives us the result 5. We observe that this is still divisible by 5. So, we once again divide 5 by 5, which gives us the result 1.

We have received result 1 at the end. Now, we cannot proceed with the division method further. So, the prime factorization of 50 is written like 2 x 5 x 5 or 2 x 5².

The prime factor tree of 50 is a special diagram that provides the pictorial representation of the prime factorization for 50. We will construct the factor tree of 50 by writing the given integer i.e. 50 at the top of a tree. Two branches will be drawn towards the two positive factors of 50. The process is repeated for the numbers at the end of each branch that is drawn until each leaf is filled with a prime number.

The factor tree of 50 is shown below:

The exponential form is an alternate method of representing repeated multiplication of the same number. Exponential notation takes the form of xⁿ, where x is multiplied by itself n time. In exponential notation, x is considered as a base, and n is known as power, exponent, or index.

As we know, the prime factorization of the 50 is 2 5 5. Accordingly, the prime factorization of 50 in exponential form is written as 2¹ x 5².

1. What is the addition and subtraction of all the factors of 50 including 50?

Solutions:

All the factors of 50 are : 1, 2,5,10, 25, 50

Addition of all the factors of 50 = 1 + 2 + 5 + 10 + 25 + 50 = 93

Hence, the addition of all the factors of 50 is 93

2. What are the Common Factors of 50 and 450?

Factors for 50 are = 1, 2,5,10, 25, and 50.

Factors for 450 are = 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, and 450

Therefore, the common factors of 50 and 450 are 1, 2, 5,10, and 25.

3. Write All the Factors of 50 Which are also the Factors of 70.

Solution :

All the factors of 50 are - 1, 2, 5,10, and 25

All the factors of 70 are - 1, 2, 5,7,14, 10, 35 and 70

Therefore, the common factors of 50 and 450 are 1, 2, 5, and 10.

FAQ (Frequently Asked Questions)

Q1. Define Common Factors.

Ans. Common factors of two or more numbers are defined as the factor that is common to both of the given numbers. For example, the common factors of 50 and 70 are 1,2, 5, and 10.

Q2. What are the Pair Factors of 50?

Ans. Pair factors of the number 50 are any two whole numbers that give the result as 50 when multiplied together. Pair factors can be both positive and negative but cannot be decimal numbers and fractions. Hence, pair factors of the number 50 are (1, 50 ), (-1, -50), (2, 25), (-2, -25), (5, 10), and (-5, -10).

Q3. How to Find the Total Number of Factors of 50?

Ans. Following are the steps to find the total number of a factor of a given number:

**Step 1****:** Find the prime factorization of 50.

Prime Factorization of 50 is = 2 x 5 x 5.

**Step 2****:** Express the prime factorization in exponent form.

Prime Factorization of 50 in exponent form = 2¹ x 5²

**Step 3:** Add 1 to each of the exponents as shown below:

Adding 1 to the exponents - (1+ 1) x (2 + 1) = 2 x 3

**Step 4****:** Multiply all the results that are obtained.

Multiplying the result - 2 x 3 = 6

This product will give you the total number of a factor of a given number. Hence, the total numbers of factors of the number 50 are 6.