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Factors of 61

When you try and find the factors of a prime number, you will always get 1 and that number as the factors. This is the fundamental rule of a prime number. Take the example of 61, the number you will study in this lesson. While there is no pop culture reference for the number, except that it is one second after a minute, there's much to learn about it.

In this lesson, we will calculate the factors of 61, prime factors of 61, and factors of 61 in pairs along with solved examples for a better understanding.

Factors of 61: 1 and 61
Prime Factorization of 61: 61

1.	What Are the Factors of 61?
2.	How to Calculate Factors of 61?
3.	Factors of 61 by Prime Factorization
4.	Factors of 61 in Pairs
5.	FAQs on Factors of 61

What are the Factors of 61?

The factor of a number is that number which divides it completely i.e. leaving no remainder. To find the factors of the number 61, we will have to perform division on 61 and find the numbers that completely divide 61, leaving no remainder.

How to Calculate the Factors of 61?

To calculate the factors of any number, in the case of 61, we need to find all the numbers that would divide 61 without leaving any remainder. We start with the number 1, then check for numbers 2, 3, 4, 5, etc up to 61, respectively. The number 1 and the number itself would always be a factor of the given number.

Refer to the following table to check division 61 by its factors:

Division	Factor
61/1	Remainder = 0 Factor = 1
61/61	Remainder = 0 Factor = 61

61 is a prime number since it has only two factors 1 and 61. A composite number has more than two factors.

Explore factors using illustrations and interactive examples

Factors of 62 - The factors of 62 are, 1, 2, 31, and 62
Factors of 63 - The factors of 63 are 1, 3, 7, 9, 21 and 63
Factors of 65 - The factors of 65 are 1, 5, 13, and 65
Factors of 66 - The factors of 66 are 1, 2, 3, 6, 11, and 66
Factors of 68 - The factors of 68 are 1, 2, 4, 17, 34, and 68

Factors of 61 by Prime Factorization

Prime factorization of a number refers to breaking down a number into the form of products of its prime factors. There are different methods that can be used to find the prime factorization of a number and hence its prime factors.

Method 1: Division Method

To find prime factors of 61 using the division method,

Step 1. Start dividing 61 from the smallest prime number i.e., 2, 3, 5, and so on. and find the smallest prime factor of the number.
Step 2. After finding the smallest prime factor of the number 61 i.e., 61 itself, divide 61 by 61 to obtain the quotient as 1.

61 ÷ 61 = 1

So, the prime factorization of 61 is 61

Method 2: Factor Tree Method

We can do the same procedure using the factor tree as shown in the diagram given below:

So, the prime factorization of 61 is 61. Further, find the products of the multiplicands in different orders to obtain the composite factors of the number.
Thus, the total factors can be written including both the prime and composite numbers together as, [1, 61]

Challenging Question:

Twin primes are a pair of prime numbers that have a difference of 2. How many pairs of twin primes are there between 1 to 61, including 61?

Factors of 61 in Pairs

Pair factors are the factors of a number given in pairs, when multiplied together give that original number. The pair factors of 61 would be the two numbers when multiplied together, result in the value 61

The following table represents the calculation of pair factors of 61:

S.No.	Positive Factor Pair	Negative Factor Pair	Pair Factorization
1.	1 and 61	-1 and -61	1 × 61 = 61

Important Notes:

Factors of 61 are 1 and 61.
Prime factorization of 61 is 1 x 61.
Positive factors of 61 are 1 and 61.
Negative factors of 61 are -1 and -61.
Factors of 61 in pairs are (1, 61) and (-1, -61).

Example 1:

Calculate the sum of all the factors of 61.

Solution:

We know, the factors of 61 are 1, and 61.
Thus, the sum of all the factors = 1 + 61 = 62
Sum of all factors of 61 is 62.
Example 2: What are the common factors of 61, 73, and 83?

Solution:

We know, factors of 61 are 1, and 61.
Factors of 73 are 1, and 73.
Factors of 83 are 1, and 83.
Thus, the common factor of 61, 73, and 83 is 1.
61, 73, and 83 are prime numbers. They have only 1 as a common factor.

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FAQs on Factors of 61

What are the prime factors of 61?

1 and 61 both are prime factors of 61.

What are the factors of 61 in pairs?

Pair factors are the factors of a number given in pairs, when multiplied together give that original number. The pair factors of 61 would be the two numbers when multiplied together, result in the value 61.
They are (1, 61) and (-1, -61).

What are the factors of 61?

Factors of 61 are 1 and 61.

What are the common factors of 61, 73, and 83?

61, 73, and 83 are prime numbers. They have only 1 as a common factor

How many factors of 61 are there?

There are two factors of 61. 1 and 61.