[Maths Class Notes] on Factors of 101 Pdf for Exam

Prime Factorization of 101

Whilst finding the pair factors, you need to find two numbers when multiplied results original number 101. 

1 x 101 = 101 which proves 1, 101 is a pair factor of 101. 

101 x 1 = 101 which proves 101, 1 is a pair factor of 101. 

Thus, we can say that both (1, 101) and (101, 1) are a positive factor of 101. 

Negative factors can be found in two steps: 

-101 x -1 = 101 which proves -101 and -1 are negative factors of 101. 

-1 x -101 = 101 which proves -1 and -101 are negative factors of 101.

 

Thus, we can say that both (-1,-101) and (-101, -1) are negative pair factors of 101. 

Can the Factor be Only One Number? 

A factor of a number can never be one number though it can be multiplication of the same digit—for instance, 8. The 8 are multiples of 1, 8, 2, 4. When we consider 2, 2 x 2 x 2 = 8. Here 2 is not a factor of a number, but 2 x 2 x 2 is the factor of 8. Always prevent accidental over factorization. The prime factorization method is the best because you can avoid duplicitous multiplication of the numbers. When you consider the number 24, the smallest number that divides 24 is 2. The smallest part is not as important as a prime number. Finding a prime number will make your work simpler. Now 12 x 2=24. The number that factorizes 12 is 6, and 6 is 2 and 3. Thus, the prime factorization of 24 is 2 x 2 x 2 x 3. 

Solved Examples

Steps to Find the Factors of 101:

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Finding prime factors of 101 can easily be done and this image shows 10 of them. 

Following are the Steps to Find the Factors of 101:

• Write the number 101. 

• Secondly, write the numbers which give results as 101. The numbers are 1 and 101, example: 1×101 = 101. 

• We now know that the prime numbers 1 and 101 are the factors that cannot be further factored. 

• The factors, therefore, are 101 and 1. 

Prime Factors: 

We know that 101 is a prime number and has only two factors, i.e., 1 and 101. The number one and the number itself when are factors are called prime numbers. So we can conclude that prime factorization of 101 is the number itself. The number of factors can be found by adding one exponentially to prime number 101. By adding, it becomes 1+1= 2. Thus, it can be concluded that 101 has two factors, and 101 has no square factor. However, the square root, when simplified, is 10.0498756. 

Are Factors of a Number Necessarily Small or can be Big?

Factors are total numbers that, when divided appropriately, results in the parent number. There are a few numbers that have more than one factorization. When a number can be factored only once, then it is called prime factors. When you are done factoring with small numbers, then try bigger numbers until you find something. If the squares of the number are bigger than what you are dividing, then only numbers that are divisible are prime. If the prime numbers are not dividing and the square of your number is bigger, the remainder will be a smaller prime number. The number left is smaller than the prime numbers that are eliminated. The number that is remaining is the prime number. Keep in mind that the number 1 is not a prime number. 

What is the List of Factors of Some Common Numbers?

The list of common factors and their prime factors are as follow: 

Factors of 36                 Factors of 68

Factors of 12                 Factors of 63

Factors of 72                 Factors of 215

Factors of 18                 Factors of 216

Factors of 98                 Factors of 17 

Factors of 80                 Factors of 150

Factors of 70                 Factors of 4