Factors

# Factors of 74 | Prime Factorization of 74 | Factor Tree of 74

Written by Prerit Jain

Updated on: 24 Aug 2023

Contents

### Factors of 74 | Prime Factorization of 74 | Factor Tree of 74

## Factors of 74

Factors of 74 | Factor Pairs of 74 | Prime factors of 74 |

1, 2, 37, 74 | (1,74) (2,37) (37,2) | 2 x 37 |

**Factors of 7**4,

**Factor Pairs of 7**4,

**Prime factors of 7**4

Calculate Factors of

**The Factors are**

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## What are the factors of 74

The factors of 74 are the numbers that can be multiplied together to give 74. The factors of 74 are 1 and 74 because 74 can be expressed as the product of 1 and 74 (1 x 74 = 74).

To find the factors of a number, you can list all of the numbers that can be multiplied together to give the original number. For example, the factors of 15 are 1, 3, 5, and 15, because 15 can be expressed as the product of the numbers 1, 3, 5, and 15 (1 x 3 x 5 x 15 = 15).

The factors of a number are all of the numbers that can be multiplied together to give the original number. For example, the factors of 74 are 1 and 74.

## How to Find Factors of 74

Here are four methods that you can use to find the factors of 74:

- Factors of 74 using the Multiplication Method
- Factors of 74 using the Division Method
- Prime Factorization of 74
- Factor tree of 74

## Factors of 74 Using the Multiplication Method

To find the factors of 74 using the multiplication method, follow these steps:

- Find two numbers that, when multiplied together, equal 74. These two numbers will be the factors of 74.
- Write down the two numbers that you found in step 1.
- Confirm that the two numbers multiply to equal 74.

For example, one pair of numbers that multiply by 74 is 1 and 74. We can confirm that these numbers are factors of 74 by multiplying them together: 1 * 74 = 74. Therefore, 1 and 74 are factors of 74.

We can also find the other two factors of 74 by using the same process: 2 * 37 = 74. Therefore, 2 and 37 are also factors of 74.

**The factors of 74 are therefore 1, 2, 37, and 74.**

## Factors of 74 Using the Division Method

Here is a method you can use to find the factors of 74 using the division method:

- Begin by dividing 74 by 2. The result is 37 with a remainder of 0. This means that 2 is a factor of 74.
- Next, divide 74 by 3. The result is 24 with a remainder of 2. This means that 3 is not a factor of 74.
- Next, divide 74 by 4. The result is 18 with a remainder of 2. This means that 4 is not a factor of 74.
- Continue dividing 74 by the integers 5 through 10. None of these integers are factors of 74.
- Finally, divide 74 by 11. The result is 6 with a remainder of 8. This means that 11 is not a factor of 74. The factors of 74 are 2 and 74. You can check your work by multiplying these two factors together to get the original number, 74.

## Prime Factorization of 74

Calculate Prime Factors of

The Prime Factors of 74 =

2 x

37

To find the prime factorization of 74, you can follow these steps:

- Begin by dividing 74 by the smallest possible prime number, which is 2. The result is 37 with a remainder of 0. This means that 2 is a factor of 74.
- Divide 37 by 2 again. The result is 18 with a remainder of 1. This means that 2 is not a factor of 37.
- Next, divide 37 by 3. The result is 12 with a remainder of 1. This means that 3 is not a factor of 37.
- Continue dividing 37 by the prime numbers 4 through 7. None of these are factors of 37.
- Finally, divide 37 by the prime number 8. The result is 4 with a remainder of 1. This means that 8 is not a factor of 37.

Since 37 cannot be further divided, we know that it is a prime number. Therefore, the prime factorization of 74 is 2 x 37. You can check your work by multiplying these two factors together to get the original number, 74.

## Factor tree of 74

- Begin by finding the smallest prime factor of 74. The smallest prime number is 2, so we will start by dividing 74 by 2. If the result is an integer (meaning there is no remainder), then 2 is a factor of 74.
- Divide the result by 2 again. If the result is an integer, then 2 is still a factor of 74. If the result is not an integer, then 2 is not a factor of 74.
- Divide the result by 3. If the result is an integer, then 3 is a factor of 74. If the result is not an integer, then 3 is not a factor of 74.
- Continue dividing the result by the prime numbers 4 through 7. If the result is an integer for any of these numbers, then it is a factor of 74.
- Finally, divide the result by the prime number 8. If the result is an integer, then 8 is a factor of 74.

If you cannot further divide the result, then it is a prime number and is a factor of 74. The factor tree is a visual representation of the process of finding the prime factors of a number. You can check your work by multiplying the factors together to see if you get the original number, 74.

## Factor Pairs of 74

Calculate Pair Factors of

1 x 74=74

2 x 37=74

37 x 2=74

So Pair Factors of 74 are

(1,74)

(2,37)

(37,2)

An integer is a whole number, and a factor of an integer is another integer that can be evenly divided into it. For example, the factors of 8 are 1, 2, 4, and 8, because these are the integers that can be evenly divided into 8.

The factor pairs of an integer are all the pairs of integers that can be multiplied together to produce that integer. For example, the factor pairs of 8 are (1, 8), (2, 4), and (4, 2).

In the case of 74, the factor pairs are (1, 74), (2, 37), (37, 2), and (74, 1). These are all the pairs of integers that can be multiplied together to equal 74.

## More Factors

- Factors of 71
- Factors of 72
- Factors of 73
- Factors of 74
- Factors of 75
- Factors of 76
- Factors of 77

## Factors of 74 – Quick Recap

**Factors of 74:**1, 2, 37, 74**Negative Factors of 74:**(-1, -2, -37, -74)**Prime Factors of 74:**2 x 37**Prime Factorization of 74:**2 x 37

## Factors of 74 – Fun Facts

- 74 is an even number, so one of its factors must be 2. In fact, 2 is a factor of 74, as well as 37 (which is half of 74).
- The prime factorization of 74 is 2 x 37. This means that 74 can be written as the product of two prime numbers (numbers that are only divisible by 1 and themselves).
- The factors of 74 can be used to find the greatest common factor (GCF) of 74 and another number. The GCF is the largest factor that two or more numbers have in common. For example, the GCF of 74 and 36 is 2, because 2 is a factor of both 74 and 36 and is the largest factor that they have in common.
- 74 is a composite number, which means it has more than two factors. In addition to 1 and 74, it also has factors 2 and 37.

**Also Check**: Multiples, Square Root, and LCM

## Solved Examples of Factor of 74

**Q.1: John has a box filled with 74 red balls, but he took 15 away. What percentage of the balls is left?****Solution: **79% of the balls are still in the box; 74-15=58 & 58/74 =0.783.

** Q.2: Steve bought 84 rolls of wrapping paper and wanted to divide them equally among 12 friends. How many rolls does each friend get? Solution:** Each friend gets 7 rolls; 84/12 =7.

** Q.3: Sarah had 87 books in her collection but gave 20 away as gifts. What percentage of books did she keep?Solution: **77% of books were kept by Sarah; 87-20= 67 & 67/87= 0.770.

**Q.4:** Jenny collected 36 rocks at the beach but found 5 more when walking home. What is the total amount of rocks now? **Solution:** The total amount of rocks Jenny now has is 41;36+5=41.

**Q.5:** Sam purchased 97 license plates for his car collection and sold 17 later that day. What percentage did he sell? **Solution: **18 % of license plates were sold by Sam;97-17 =80 & 80/97= 0 .824 (with a very small remainder).

**Q.6:** Ellen bought 25 pairs of shoes from the store, but only kept 16 pairs, what percentage was returned? **Solution:** 36 %of Ellen’s purchase was returned;25-16 = 9& 9/25 = 0 .36 (with no remainder ).** Q.7: Patrick wanted to distribute 54 doughnuts** among 8 children how many doughnuts should each child receive?

Solution: Each child should receive 6 doughnuts; 54 / 8 = 6.

**Q.8:** Jacob has 42 playing cards which he wants to separate into piles, how many piles will he have if each pile contains 7 cards? **Solution: **Jacob will have six piles; 42 / 7 = 6 with no remainder.

** Q.9: Josh purchased 32 candy bars at 5 bars per dollar, how much did he spend? Solution: **Josh spent $160 Dollars; 32 * 5 = 160

** Q.10: Lisa picked up 96 stones while walking along the riverbank, but 4 fell in the water what percentage was lost? **

**Solution:**4.2% of Lisa’s stones were lost; 96 – 4 = 92& 92/96= 0 .958.

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## Frequently Asked Questions on Factors of 74

**What is the greatest common factor between 74 and 36?**

The greatest common factor (GCF) of 74 and 36 is 2, as both 74 and 36 are divisible by 2 without a remainder.

**How many factors does 74 have?**

There are 8 factors of 74; 1,2,37,74, -1,-2,-37,-74.

**What are all the prime factors of 74?**

All the prime factors of 74 are 2 and 37; 2 x 37 = 74.

**What two numbers add up to 74?**

Two numbers that add up to 74 include 18 and 56; 18 + 56 = 74

**What number can divide 74 evenly?**

Any number from 1-74 can divide into 74 with no remainders, but some will produce fractions or decimals instead of a whole number result.

**Is there a difference between the factors and multiples of 74?**

While factors and multiples have similar definitions in that they both refer to groups or collections of related numbers generated by multiplying or dividing a given number, there is an important difference between them – factors refer to how many times the original number can be divided evenly while multiples make reference to how many times it has been multiplied by itself.

**What is the sum of all positive integer divisors for 74?**

The sum of the positive integer divisors for 74 is 114; 1+2+37+74=114

**What Are Some Examples Of Factors Of 74?**

Some examples of factors of 7 4 include 1,2,37 and 74.

Written by

Prerit Jain