Factors of 61 | Prime Factorization of 61 | Factor Tree of 61

Factors of 61: Factors are a set of integers that can divide a given number evenly, without leaving a reminder.

The number 61 is a prime number. It has only two factors, 1 and 61.

Factors can be written in both positive and negative formats. They can also occur as pairs. This means that multiplying the numbers within the pairs will yield a product that equals the given number.

In this post, we will find the factors of 61 using the division method, prime factorization, and factor tree method. Continue reading to learn more.

Looking to Learn Math? Book a Free Trial Lesson and match with top Math Tutors for concepts, homework help, and test prep.

What Are the Factors of 61?

The factors of 61, like that of other numbers, divide 61 evenly without leaving any remainder. The factors can be positive and negative. Hence, the number 61 has both positive and negative factors.

Factors of 61: 1 and 61

Negative Factors of 61: –1 and -61

Prime Factorization of 61:  61 X 1 or 611

Pair Factors of 61: (1, 61)

Prime Factors of 61: 61

Sum of Factors of 61: 62

Sum of Prime Factors of 61: 61

What Are the Factors of 61 in Pairs?

 The pair factors of 61 are a combination of two numbers, which when multiplied by each other give 61 as a product. These pair factors are also written in positive and negative pairs as shown in the table below:

Positive Pair Factors of 61

Positive pair factor of 61: (1, 61)

 

Negative Pair Factors of 61

Negative pair factor of 61: (-1, -61).

How To Find Factors of 61 Through Division Method?

We are using the division method to determine the factors of 61. As per this approach, we will multiply 61 with a sequence of natural numbers. The numbers that divide 61 evenly are known as its factors. The following steps give a detailed account of how to find the factors of 61 using the division method

61 ÷ 1 = 61

61 ÷ 61 = 1

Therefore, we can see that 1 and 61 are the numbers that do not leave any remainder when divided by 61. 

What Is the Prime Factorization of 61?

Before we use the prime factorization method, we must check if the given number is a prime number. If the number is a prime number, then it has only two factors: 1 and 61. If not, then it has more than two factors.

61 is a prime number. It has only two factors. But let us employ the prime factorization method to present a better understanding of the concept.

The steps below help find the factors of 61 using the prime factorization method are given below:

Step 1: Divide 61 by the smallest prime number that can divide it. This number is 61.
61 ÷ 61 = 1

Step 2: Now we got 1 as the quotient. This brings us to the end of the factor tree.
Since 1 cannot be divided further, the prime factor of 61 is 61¹.

Image representation of the prime factorization of 61:

What is the Factor Tree of 61?

The third method of finding the factors of 61 is the factor tree method. This method will place the number 61 on top of the factor tree. Now, as part of the branches, we will write down any set of pair factors of the given number 61. We will again split the pair of factors into factors. This process will go on until the branches become prime numbers.

Step 1: Let’s place the number 61 at the top of the factor tree. Since it is a prime number, the only two factors of 61 are 1 and 61.

Step 2: We cannot separate these numbers into branches anymore. The branches in the factor tree will now be all the prime numbers.

Hence, circling all the branches, 61¹ or 61 X 1 = 61, which are 61 prime factors.
Below is an image representation of the factor tree of 61, choosing 1 and 61 as branches.

Solved Examples of Factors of 61

Here are some solved examples of 61 factors:

What is the sum of all the factors of 61?
1 and 61 are the 61 factors.
1 + 61 = 62
Hence, 62 is the sum of all 61 factors.

What are the factors and prime factors of 61?
The factors of 61: 1 and 61.
The prime factors of 61: 61 X 1 or 61¹.

What’s the highest common factor between 70 and 61?
The factors of 61 are 1 and 61.
Factors of 70 are 1, 2, 5, 7, 10, 14, 35 and 70.
Hence, from the above, the highest and only common factor of 61 and 70 is 1.

What’s the highest common factor between 18 and 61?
The factors of 18 are 1, 2, 3, 4, 6, 9, 18.
Factors 61 are 1 and 61.
Hence, from the above, the highest and only common factor of 18 and 61 is 1.

What are the factors of -61?
The factors of -61 are -1 and -61.

What are the common factors of 61 and 610?
To find the common factors of 61 and 610, we need to find the factors of both numbers.
Factors of 61: 1 and 61
Factors of 610: 1, 2, 5, 10, 61, 122, 305 and 610
Hence the common factor of 61 and 610 is 1.

What are all the factors of 61?
The factors of 61 are 1 and 61.

What are the factors of 61 that are composite?
Any number which has more than 2 factors is known as a composite number. 61 does not have any composite factors.

How many 61 factors are odd?
All the factors of 61 are odd. They are 1 and 61.

How many different factors are there for the number 61?
A total of 2 factors are there for the number 61 and they are 1 and 61.

How many pair factors are there in 61?
A total of 1 pair is there in factors of 61.

What is the largest factor of 61?
The largest factor of 61 is 61.
The second largest factor of 61 is 1.

Looking to Learn Math? Book a Free Trial Lesson and match with top Math Tutors for concepts, homework help, and test prep.

FAQs on Factors of 61

List all the factors of 61
1 and 61 are the 61 factors.

What are the composite factors of 61?
61 is a prime number so, it has no composite factors.
Composite factors are those that have more than 2 factors other than 1 and itself.

What are the factors of 61 in pairs?
(1, 61) is the 61 factors of pair.

What are the positive factors for 61?
1 and 61 are the positive factors for 61.

Is 305 a factor of 61?
305 is not a factor of 61. But it is a multiple of 61.
61 X 5 = 305