Factors of 51: Prime Factorization, Methods, Tree, and Examples

Factors of 51 are those numbers that, when multiplied together, equal to 51 or by which 51 can completely be divided in half. Therefore, a number divides 51 with a 0 as the remainder is considered a factor.
Factors of fifty one

Figure 1 – All possible Factors of 51

To analyze factors, list all the numbers that are less than or equal to the number you’re looking for. The numbers for 51, for instance, will range from 1 to 17. If so, the answer can be found by dividing each of them.  The claim that two is the factor of all numbers is an exceedingly fascinating truth about factors. Furthermore, one can discover a number’s factors using division and multiplication. Finding factors of integers can be done in many ways, though. The factors of a number can be determined in much more straightforward modes.  Once the remainder equals zero, which can be obtained by just reducing the number itself until the remainder equals zero, the quotient and the divisor are considered as factors of the provided number. Let’s use one of these cases as an example. When 51 is divided by 3, the result is 17. The answer and the divisor are therefore both viewed as factors. As a group, they are referred to as factor pairs, i.e. (3, 17). This article will answer all of your inquiries about the factors of 51, including how to discover factor pairs, simple and direct solutions, entertaining random facts, and the prime factorization of 51. 

What Are the Factors of 51?

The Factors of 51 are 1, 3, 17, and 51. These numbers can never produce a remainder other than zero when 51 is divided by them.  To create factor pairs, these factors can all be combined. Pair the numbers together, so the outcome is 51, and you’ll get it. Pair factors of 51 are (1, 51) and (3, 17).  Because 51 is a composite number, there are four factors in all.

How to Calculate the Factors of 51?

To calculate the factors of 51, we may use the techniques described at the beginning of this article, which are Division and Multiplication. Always remember that a number must be divided by another, leaving a zero-valued remainder to be a factor of 51, and the divisors must only give whole number quotients. If the number yields a decimal result, It won’t be considered either. Below is the division method to find out the factors of 51: You can divide 51 by the smallest divisor you can find, which is 1. As a result, 1 is one of the factors of 51. The ability of the following whole number to divide 51 in half is then checked. \[ \frac{51}{2} = 25.5 \] Hence, 2 is not a factor of 51. \[ \frac{51}{3} = 17 \] This shows that 3 is a factor of 51. Moving on, we test the next few numbers. \[ \frac{51}{4} = 12.75 \] \[ \frac{51}{7} = 7.28 \] Thus, they are not the factors of 51. Once 51 divided by 51 equals 1, we can stop dividing by whole numbers. We are therefore unable to use any more whole numbers. Factors of 51 found out through division are as follows: \[ \frac{51}{51} = 1 \] \[ \frac{51}{3} = 17 \] Therefore these are the factors of 51, i.e., 1, 3, 17, and 51. Now let’s find factors of 51 by concentrating on multiplication. Consider 51 as the result of two whole numbers in all possible ways. Every integer found in any of these products is a factor of 51. Here are a few examples: 1 × 51 = 51 3 × 17 = 51 17 × 3 = 51 51 × 1 = 51 Thus, stated above are the factors of 51.

Factors of 51 by Prime Factorization

The only way to represent a number as the sum of its prime factors is through prime factorization. It entails figuring out which prime factors can multiply with one another to produce the given number.  Put another way; it is a method for determining or showing a given integer as the sum of prime integers. There are only two factors to a prime number: one and the number itself. Since 51 is a composite number, it should contain prime factors. 51 = 3 x 17 is the Prime factorization of 51. It is evident from the prime factorization of 51 that the factors of 51 are 3 and 17. In actuality, the prime factors of 51 are 3 and 17. When the factors of 51 are 3 and 17, then 3 x 17 = 51 is likewise a factor of the number 51. We also know that every number has 1 as a factor. Therefore, 1, 3, 17, and 51 are the prime factors of 51.  The prime factorization is 3 x 17. Let’s take a look at the diagram of the prime factorization of 51:
Prime factorization of fifty one

Figure 2 – Prime Factorization of 51

Factor Tree of 51

A Factor tree is one approach to express factors in terms of prime factors, which is one of several ways to display prime factors of a number graphically.   The root of the factor tree is the actual number, and until you get to the prime number, and until you get to the prime number, the branches that come out of the root are the factors.  Consequently, 3 and 17 are 51’s prime factors by prime factorization. Take a look at the diagram of Factor Tree:
Factor tree of fifty one

Figure 3 – Factor Tree of 51

Listed below are incredible facts about the integer 51:
  1. 51 is a pentagonal number, an 18-goal number, and a centered pentagonal number.
  2. The sixth Motzkin number, 51, indicates how many different methods there are to connect any six points along a circle’s edge without drawing an intersecting chord, regardless of where the points are on edge.
  3. After the numbers 22, 29, and 39 in the sequence, 51 is a Perrin number.
  4. Area 51, a piece of territory under the jurisdiction of the US military in Southern Nevada, is thought to have a top-secret aircraft testing facility.
  5. Antimony’s atomic number is 51.
  6. The number to reach Peru with direct international dialing.
  7. The number of articles Alexander Hamilton penned supported the US constitution for The Federalist Papers.
  8. Doc Hudson’s number in the 2006 motion picture Cars was 51.
  9. The P-51 Mustang fighter plane’s model number from World War II.
  10.  In the 1950s, Photo 51, a vital X-ray image, helped to clarify the structure of DNA.

Factors of 51 in Pairs

Factors of 51 are two numbers that, when multiplied together, equal the number 51. The factor pairings are as follows: The pair factor of 51 if 51 x 1 = 51 is (51, 1). Let’s look at some more pairs, too: 1×51 = 51, (1, 51) is a pair factor of 51. 3×17 = 51, (3, 17) is a pair factor of 51. 17×3 = 51, (17, 3) is a pair factor of 51.  Thus, listed above are the positive factor pairs of 51. Reversing the signs is all that is necessary to determine the negative factor pair. The following are the negative factor pairings: -1x-51 = 51, (-1, -51) is a pair factor of 51. -3x-17 = 51, (-3, -17) is a pair factor of 51. -17x-3 = 51, (-17, -3) is a pair factor of 51.  -51x-1 = 51, (-51, -1) is a pair factor of 51.

Factors of 51 Solved Examples

Example 1

Find the sum of all the factors of 51.

Solution

Factors of 51: 1, 3, 17 and 51

1 + 3 + 17 + 51 = 72

Thus, the sum of all the factors of 51 is 72.

Example 2:

Emma got an MCQ practice sheet as homework. In an MCQ, she has to choose the correct option for the common factors between 51 and 60. She has three options to choose from. The options are:
  1. 1, 3 and 9
  2. 1 and 3
  3. 1, 2 and 4
Help Emma find the common factors between 51 and 60.

Solution

Factors of 51: 1, 3, 17, and 51. Factors of 60:  1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60. Hence, the common factors between 51 and 60 are 1 and 3. Therefore, Emma will choose option b as the correct answer. 

Example 3

Multiply and subtract all the factors of 51.

Solution

Multiplication: Factors of 51: 1, 3, 17 and 51

1 x 3 x 17 x 51 = 2,601

Thus, the answer is 2,601. Subtraction: Factors of 51: 1, 3, 17 and 51

51 – 17 – 3 – 1 = 30

Hence, the answer is 30.

Example 4

Elle prepared the chocolate chip cookie dough, making 51 cookies for her birthday bash. She wants to give away these cookies as goodie bags to her friends. 17 of her friends are invited to the party. How many cookies should Elle put in each goodie bag?

Solution:

\[ \frac{51}{17} = 3 \] The answer is 3. Therefore, Elle should put 3 cookies per goodie bag. All the images/diagrams are created using GeoGebra.

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