Factors

# Factors of 133 | Prime Factorization of 133 | Factor Tree of 133

Written by Prerit Jain

Updated on: 30 Jun 2023

Contents

### Factors of 133 | Prime Factorization of 133 | Factor Tree of 133

## Factors of 133

Factors of 133 | Factor Pairs of 133 | Prime factors of 133 |

1, 7, 19 and 133 | (1, 133) and (7, 19) | 7 x 19 |

**Factors of 133**,

**Factor Pairs of 133**,

**Prime factors of 133**

Calculate Factors of

**The Factors are**

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## What are the factors of 133

Discover the factors of 133—it’s easy! Start by making a list with all the whole numbers from 1 to 133. Next, divide each number in your list into 134 and check if it has no remainders – this way you’ll find out which ones are the factors of 133! The four answers will be 1, 7, 19, and 133. Give it a try yourself for some fun math exploration!

## How to Find Factors of 133

The major methods of finding the factors of 133 are as follows:

- Factors of 133 using the Multiplication Method
- Factors of 133 using the Division Method
- Prime Factorization of 133
- Factor tree of 133

## Factors of 133 Using the Multiplication Method

Factors are the numbers that multiply together to form a certain number. To find out which factors belong to 133, we can use the multiplication method. All you have to do is take 1 and it’s a friend (133) and join them up in pairs; then just multiply both of them together until each pair makes 133. That way, you’ll discover that those same two friends 1 & 133 are actually its only set of factors!

## Factors of 133 Using Division Method

To find the factors of 133 using the division method, follow these steps:

- Start with the number 1 as a potential factor.
- Divide 133 by 1. 133 ÷ 1 = 13.
- Check if the result is a whole number. If it is, then 1 is a factor of 133.
- Repeat the process with the next potential factor, which is 2. 133 ÷ 2 = 66.5 (not a whole number).
- Move on to the next potential factor, which is 3. 133 ÷ 3 = 44.33 (not a whole number).
- Continue this process, dividing 133 by each subsequent number, until you reach the square root of 133 or the halfway point.
- 133 ÷ 4 = 33.25 (not a whole number)
- 133 ÷ 5 = 26.6 (not a whole number)
- 133 ÷ 6 = 22.17 (not a whole number)
- 133 ÷ 7 = 19 (whole number)
- Check if the number you divided by is a factor. If it is, then write down both the divisor and the quotient as factors of 133.
- 7 is a factor of 133: 7 × 19 = 133
- Continue dividing by larger numbers until you reach the halfway point or the square root of 133.
- 133 ÷ 8 = 16.625 (not a whole number)
- 133 ÷ 9 = 14.77 (not a whole number)
- 133 ÷ 10 = 13.3 (not a whole number)
- At this point, you can stop because you have reached the halfway point of 133 (approximately).

**The factors of 133 are 1, 7, 19, and 133.**

Using the division method, you can find the factors of any number by systematically dividing it by potential factors and checking for whole number results.

## Prime Factorization of 133

Calculate Prime Factors of

The Prime Factors of 133 =

7 x

19

To find the prime factorization of 133, we must take a step-by-step approach.

- Start with the number 2, the smallest prime number.
- Divide 133 by 2: 133 ÷ 2 = 66.5 (not a whole number).
- Move on to the next prime number, which is 3.
- Divide 133 by 3: 133 ÷ 3 = 44.33 (not a whole number).
- Continue dividing by prime numbers until the quotient is 1.
- Divide by 5: 133 ÷ 5 = 26.6 (not a whole number).
- Divide by 7: 133 ÷ 7 = 19 (whole number).
- At this point, the quotient is 1, indicating that we have found all the prime factors of 133.
- Write down the prime factors that were used in divisions: 7, 19.
- The prime factorization of 133 is the product of these prime factors: 7 × 19.

**Therefore, the prime factorization of 133 is 7 × 19.**

## Factor tree of 133

Prime factorization is a useful Math tool for understanding which numbers are divisible by each other. To use it, we must first find the smallest prime number less than or equal to the square root of our starting value – in this case 133. We do so and discover that 2 is not a factor; then move onto 3 and again determine that it’s also not relevant before finally dividing into 5–the resulting answer with no remainder tells us there’s an even distribution between these two values!

Now begin breaking down those until you can’t break them anymore. Learning to factor and prime factorize a number can be an essential skill in Mathematics! Let’s look at the example of finding the factors, prime factorization, and creating a factor tree for 133. If we divide 133 by 7, we get 19 with no remainder; this tells us that 7 is one of its factors. We then take those two numbers (19 and 7) which are their own facts first before going on to find all the rest of the factoring possibilities until you reach just Prime Factors or 1 x something left – so in our case, it’s simply:

7 * 19 =133 as your answer from Factoring out each side equal together. To draw up a Factor Tree for 133, start by writing down ‘133’ horizontally across before drawing downwards off it two vertical lines – end these two with either end written as ‘7 & 19’ respectively representing both sides being divided evenly when adding them back together again like pieces making up part of the puzzle do make the whole picture complete!

## Factor Pairs of 133

Calculate Pair Factors of

1 x 133=133

7 x 19=133

19 x 7=133

So Pair Factors of 133 are

(1,133)

(7,19)

(19,7)

If you wanted to divide 133 evenly into separate pieces, who would be the lucky recipients? Well, it turns out that there are 4 divisors of 133: 1, 7, 19, and…133! The number 133 has two-factor pairs: (1, 133) and (7, 19). These factor pairs are formed by multiplying two numbers together to yield the value of 133. The first factor pair consists of the numbers 1 and 133, which when multiplied together give the result of 133. Similarly, the second-factor pair comprises the numbers 7 and 19, which also multiply to give 133. These factor pairs represent the divisors of 133, showcasing the numbers that evenly divide into them.

## More Factors

## Factors of 133 – Quick Recap

**Factors of 133:**1, 7, 19, and 133.**Negative Factors of 133:**-1, -7, -19, -133.**Prime Factors of 133:**7 x 19**Prime Factorization of 133:**

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

## Solved Examples of Factor of 133

**Q.1: If one family has 133 books, and another family has 11 books, how many times more books does the first family have?****Solution: **12 times more books (133 ÷ 11 = 12).

**Q.2: A charity is collecting donations for a new building project, and they need to raise exactly 133 dollars to break ground. If each person gives 11 dollars, how many people need to donate in order to meet their goal? **** Solution: **12 people (133 ÷ 11 = 12).

**Q.3:** Amy needs to print out 133 pages for her school project, but her printer can only print 10 pages at a time. How many times will she need to reload the printer paper? ** Solution: **33 pages ÷ 10 pages = 13.3. Since we cannot have a fraction of a reload, we need to round up to the nearest whole number because Amy cannot reload the paper a fraction of a time. Rounding up 13.3 to the nearest whole number gives us 14. Therefore, Amy will need to reload the printer paper 14 times to print out 133 pages for her school project.

**Q.4:** A bus has 133 seats and 126 people are boarding it. Is it possible to let everyone board without breaking any seat limits? **Solution:** In this case, 133 seats ≥ 126 people. Therefore, it is possible to let everyone board the bus without breaking any seat limits, as there are enough seats for the 126 people boarding.

**Q.5:** Vivian got a cash reward of $133 for winning an award, and she wants to evenly split this money among**7 friends. How much money will each of them get? ****Solution:** $133 ÷ 7 = $19. Therefore, each friend will receive $19.

** Q.6: Georgina wants to bake a batch of muffins using 130 grams of sugar but only knows recipes that call for 10 grams at a time. How many muffins will she be able to make from this amount of sugar? Solution:** 13 muffins (130 ÷ 10=13)

**Q.7:** **A family reunion consists of 13 people so every family brings 11 food items. How many food items do they bring altogether? Solution: **143 food items (13×11=143 )

**Q.8:****Jane buys 135 pencils each costing 5 cents less than each pen she purchases which costs 15 cents What is the total cost for all pencils? Solution: **Determine the cost of each pen, which is given as 15 cents. Determine the cost of each pencil by subtracting 5 cents from the cost of each pen. In this case, each pencil costs 15 cents – 5 cents = 10 cents. Multiply the cost of each pencil by the total number of pencils, which is given as 135 pencils. Perform the calculation: 10 cents × 135 pencils = 1350 cents. The total cost for all the pencils is 1350 cents.

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## Frequently Asked Questions on Factors of 133

**What are the factors of 133?**

The factors of 133 are 1, 7, 19, and 133.

**How do you find the factors of 133?**

To find the factor of a number, simply divide the number by each number between 1 and itself until you cannot go any further without getting a decimal or fractional answer.

**How many factors does 133 have?**

There are four factors for 133: 1, 7, 19, and 133.

**What is the prime factorization of 133?**

The prime factorization of 133 is 7 x 19.

**What is a factor tree for 133?**

A Factor Tree for 133 would look like this:

133 / \ 7 19

**Is 26 a factor of 133?**

No, 26 is not a factor of 133 (133 ÷ 26 = 5.12).

**Is 66 a factor of 133?**

No, 66 is not a factor of 133 (133 ÷ 66 = 2 with remainder 5).

**Is 135 a factor of 133?**

No, 135 is not a factor of 133 (133 ÷ 135 = 0 with remainder 33).

Written by

Prerit Jain