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What are The Factors of 74?

Factoring Method

Last updated date: 29th Jan 2023
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Factoring is the process of looking for factors in a mathematical expression to make it look like a multiplication problem. Factoring works by reversing the multiplication process. Finding two numbers to multiply to produce another number is as simple as factoring. The six factoring methods are as follows:

  • Greatest Common Factor (GCF)

  • Grouping Method.

  • Sum or difference in two cubes.

  • The difference in the two squares method.

  • General trinomials.

  • Trinomial method.


What are The Factors of 74?

Natural numbers that evenly divide the actual number are called factors of 74. Because 74 is an even number, it is divisible by two (by divisibility rules). As a result, the number 2 divides the original number in half. The factors are also known as the 74 divisors. Such values are the required factors if the product of two whole numbers equals 74. Since 74 is a composite number, it must have more than two elements. The numbers that provide the result of 74 when multiplied in pairs are known as 74 factors.


The numbers that completely divide a number n are called its factors. It means that a is the factor of n if the residual in n/a is zero. We're discussing the elements of the number 74 right now. Let's start with the numbers that divide 74 completely.


The positive numbers are 1, 2, 37, and 74, which divides 74. As a result, the positive factors for 74 are 1, 2, 37, and 74, whereas the negative factors are -1, -2, -37, and -74.


How to Calculate the Factors of 74?

The factors are all the numbers that divide 74 without leaving a remainder.

Let's see if we can divide 74 by counting numbers (1,2,3 etc, and see when the remainder is 0).

1 is a factor of 74 because the quotient equals 74 and the remainder equals 0.

Since 74 is an even number, 2 divides it evenly with no remainder.


2 is a factor of 74 since the quotient is 37 and the remainder is 0.

Coming on, we can see that the numbers 1, 2, 37, and 74 divide 74 perfectly, leaving no remainder.


Image:


Finding Positive Factors of 74


Now here is list the factors of 74 is as follows,


Division Method

Multiplication Method

74 ÷ 1 = 74

1 x 74 = 74

74 ÷ 2 = 37

2 x 37 = 74

74 ÷ 37 = 2

37 x 2 = 74

74 ÷ 74 = 1

74 x 1 = 74


Therefore, the factors of 74 are 1, 2, 37 and 74.


What is The Prime Factorization of 74?

We write 74 as a product of prime numbers using the prime factorization method.

Prime numbers are those with only two factors: one and the number itself. For instance, 2, 3, 5, 7, 11, and 13 are all numbers.


The following figure is the factor tree of 74:


Image


Important Notes:

  • Factors of 74 number are 1, 2, 37 and 74

  • The 74 number is a semiprime number as it can be expressed as a product of two prime numbers.

  • If a number n has an odd number of (+ve) positive factors then n is a perfect square.

  • There are no factors of a number n between (n, n2).


Solved Examples

Ex.1. Help Donald to calculate the sum of all the positive factors of 74 numbers.

Solution:

The positive factors of 74 numbers are: 1, 2, 37, and 74. Therefore, the sum of all the factors of 74 is 1 + 2 + 37 + 74 = 114.

Hence, Sum of all the positive factors of 74 numbers is 114.


Ex.2. Shelly wants to add a natural number to 30 so that it will become a factor of 74, what number should she add.

Solution:

Let's suppose she adds x to 30. So x + 30 is a factor of 74.

Let's write down all the factors of 74 greater than 30: (37, 74)

x + 30 = 37

x = 37 - 30 = 7

or

x + 30 = 74

x = 74 - 30 = 44

So,The value of x can be 7, 44.


Ex.3. Find the common factors of 72, 74 and 86.

Solution:

The factors of 72 number is 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72

The factors of 74 numbers are as follows 1, 2, 37, and 74.

The factors of 86 numbers are as given 1, 2, 43, and 86.

Hence, the factors common to 72, 74 and 86 are 1 and 2.


Practise Question MCQs

1. The Prime factor of the composite number 74 are

  1. 1

  2. 3, 37

  3. Both A and B

  4. 741

Ans: B


2. 74 is a _____

  1. Even number

  2. Prime number

  3. Composite number

  4. Both A and C

Ans: D


Conclusion

In this article, we have learned to calculate the factors of 74, prime factors of 74, and factors of 74 in pairs along with some of the solved examples for a better understanding.

FAQs on What are The Factors of 74?

1. What is a factor tree?

A factor tree is a visual representation of a number's various factors and subfactors. Its purpose is to make factorization simpler. It's made by identifying the factors of a number, then calculating the factor of the factors of a number.  The method is repeated until you have a large number of prime factors, which is the prime factorization of the original number. Remember to remember the second component is a factor pair when constructing the tree.

2. What is the prime factorization of 74?

The result of factoring a number into a set of components, each of which is a prime number, called a prime factorization. In most cases, 74 is stated as a product of its prime factors.

 

This is the result for 74: 2 x 37 = 74

3. What are multiples of 74?

Multiples of 74 numbers are 74, 148, 222, 296, 370, 444, 518, 592, 666, 740 and so on.

4. What are the prime factors of 74?

Factors of 74 number are: 1, 2, 37 and 74.

Prime Factorization of 74: 74 = 2 × 37.


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