Didyou know that 600is an even composite number having 24 divisors constituting of the first threeprime numbers 2, 3, and 5?In this chapter, we will calculate the factors of 600, prime factors of 600, and factors of 600in pairs along with solved examples for a better understanding.
- Factors of 600: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, and 600
- Prime Factorization of 600:600= 2× 2× 2× 3× 5× 5= 23× 3× 52
| 1. | What Are the Factors of 600? |
| 2. | How to Calculate the Factors of 600? |
| 3. | Factors of 600 by Prime Factorization |
| 4. | Factors of 600 in Pairs |
| 5. | FAQs on Factors of 600 |
What Are the Factors of 600?
Factors of 600 are the numbers which on multiplication give the product as 600.Thefactors of 600are thenumbers that divide it without leaving any remainder. So, when any two whole numbers aremultipliedwith each other and600 is obtainedas the answer, it is said thatboth these numbers are the factors of 600.
How to Calculate the Factors of 600?
We calculate the factors of 600 byfinding all the numbers which would divide 600without leaving any remainder. 600 can be expressedas a product of its prime factors in the prime factorization method, and wedivide 600 with its divisors in the division method. Hence, the divisors, as well as their quotients, are the factors of 600.
| Numbers Dividing 600 | Factors of 600 |
|---|---|
| 600/1 = 600 | 1 and 600 are factors of 600. |
| 600/2 = 300 | 2 and 300 are factors of 600. |
| 600/3 = 200 | 3 and 200 are factors of 600. |
| 600/4 = 150 | 4 and 150 are factors of 600. |
| 600/5 = 120 | 5 and 120 are factors of 600. |
| 600/6 = 100 | 6 and 100 are factors of 600. |
| 600/8 = 75 | 8 and 75 are factors of 600. |
| 600/10 = 60 | 10 and 60 are factors of 600. |
| 600/12 = 50 | 12 and 50 are factors of 600. |
| 600/15 = 40 | 15 and 40 are factors of 600. |
| 600/20 = 30 | 20 and 30 are factors of 600. |
| 600/24 = 25 | 24 and 25 are factors of 600. |
Hence,the factors of 600are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, and 600.
Explore factors using illustrations and interactive examples.
- Factors of 300- The factors of 300are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, and 300.
- Factors of 150- The factors of 150are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150.
- Factors of 75- The factors of 75are 1, 3, 5, 15, 25, and 75.
- Factors of 54- The factors of 54are 1, 2, 3, 6, 9, 18, 27, and 54.
- Factors of 50- The factors of 50are 1, 2, 5, 10, 25, and50.
- Factors of 24- The factors of 24are 1, 2, 3, 4, 6, 8, 12, and 24.
Factors of 600 by Prime Factorization
Prime factorization is referred to as expressing a composite number as the product of itsprime factors. To get the prime factorization of 600, we can use two methods:
- Method 1: Factor Tree Method
- Method 2: Upside-Down Division Method
Method 1: Factor Tree Method
The factor tree of 600is:
Method 2: Upside-Down Division Method
On dividing 600 by its smallest prime factor which is 2 we get,
600/2= 30
300 is now divided by its smallest prime factor and the quotient is obtained. This process is repeated till we get the quotient as 1.
The prime factorization of 600:
Hence, the prime factors of 600are2, 3, and 5.
The prime factorization of 600is2× 2× 2× 3× 5× 5.
Factors of 600 in Pairs
Numberswhich on multiplication to each other give 600are known as the factor pairs of 600. Let's observe the following table havingfactorsof 600in pairs. If we consider negative integers, then both the numbers in the pair factors will be negative as ( - ve × - ve ) = +ve.
| Positive Pair Factors of 600 | Negative Pair Factors of 600 |
|---|---|
| (1, 600) | (-1, -600) |
| (2, 300) | (-2, -300) |
| (3, 200) | (-3, -200) |
| (4, 150) | (-4, -150) |
| (5, 120) | (-5, -120) |
| (6, 100) | (-6, -100) |
| (8, 75) | (-8, -75) |
| (10, 60) | (-10, -60) |
| (12, 50) | (-12, -50) |
| (15, 40) | (-15, -40) |
| (20, 30) | (-20, -30) |
| (24, 25) | (-24, -25) |
Important Notes:
- The sum of the digits of 600is 6. As 6is divisible by 3, 3is one of the factors of 600.
- 600 is not a perfect square number. Thus, it has even number of factors.
FAQs on Factors of 600
What are thefactorsof 600?
The factors of 600are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, and 600.
What are the prime factors of 600?
The prime factors of 600are 2, 3, and 5.
Which factors of 600 are perfect squares?
The factors of 600 which are perfect squares are 1,4, 25, and 100.
What are the common factors of 600and 450?
The factors of 600are1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, and 600.
The factors of 450are1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, and 450.
Hence, the common factors of 600and 450are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150.
What are the negative pair factors of 600?
The negative pair factors of 600 are(-1, -600), (-2, -300), (-3, -200), (-4, -150),(-5, -120), (-6, -100), (-8, -75), (-10, -60), (-12, -50),(-15, -40), (-20, -30), and (-24, -25).
