The distinct factors of 1000 are the numbers which when dividing 1000 leaves the remainder zero. The number 1000 has several factors andalso is an even composite number.In this lesson, we will calculate the factors of 1000, prime factors of 1000,and factors of 1000 in pairs along with solved examples for a better understanding.
Factors of 1000: 1 2,4,5, 8,10,20,25,40,50,100,125, 200,250, 500,and 1000.
Prime Factorizationof 1000: 1000 = 2 × 2 × 2 × 5 × 5× 5.
| 1. | What Are the Factors of 1000? |
| 2. | Important Notes |
| 3. | How to Calculate Factors of 1000? |
| 4. | Factors of 37 by Prime Factorization |
| 5. | Factors of 1000 in Pairs |
| 6. | FAQs on Factors of 1000 |
What Are the Factors of 1000?
The factor of a number is that number that divides it completelyi.e., it leaves no remainder. To find the factors of the number 1000, we will have to performdivisionon 1000and find the numbers which divide 1000completely, leaving no remainders.
How to Calculate the Factors of 1000?
To calculate the factors of any number, say 1000,we need to find all the numbers that would divide 1000without leaving any remainder. We can start with the number 1, then check for numbers 2, 3, 4, 5, 6, 7, etc. up to 500(approximatehalf of 1000). The number 1 and the number itself will always be a factor of the given number.
The following table showsdivision of 1000by itsfactors:
| Division | Factor |
|---|---|
| 1000÷ 1 | Remainder = 0,Factor = 1 |
| 1000 ÷ 2 | Remainder = 0,Factor = 2 |
| 1000÷ 4 | Remainder = 0,Factor = 4 |
| 1000÷ 5 | Remainder = 0,Factor = 5 |
| 1000 ÷ 8 | Remainder = 0,Factor = 8 |
| 1000÷ 10 | Remainder = 0,Factor = 10 |
| 1000÷ 20 | Remainder = 0,Factor = 20 |
| 1000÷ 25 | Remainder = 0,Factor = 25 |
| 1000÷ 40 | Remainder = 0,Factor = 40 |
| 1000÷ 50 | Remainder = 0,Factor = 50 |
1000÷ 100 | Remainder = 0,Factor = 100 |
1000÷ 125 | Remainder = 0,Factor = 125 |
| 1000÷ 200 | Remainder = 0,Factor = 200 |
1000÷ 250 | Remainder = 0,Factor = 250 |
1000÷ 500 | Remainder = 0,Factor = 500 |
1000÷ 1000 | Remainder = 0,Factor = 1000 |
Hence, the factors of 1000are 1, 2,4,5, 8,10,20,25,40,50,100,125, 200,250, 500, and 1000.
Explore factors using illustrations and interactive examples
- Factors of 100- The factors of 100 are 1, 2, 4, 8, 10, 20, 25, 50, and 100
- Factors of 110- The factors of 110 are 1, 2, 5, 11, 22, 55, and 110
- Factors of 200- The factors of 200 are1, 2, 4, 8, 10, 20, 25, 50, 100 and 200
- Factors of 400- The factors of 400 are 1, 2, 4, 8, 10, 20, 25, 50, 100, 200,and 400
- Factors of 900- The factors of 900 are 1, 2, 3, 4, 5, 6, 10, 15, 20, 25, 30, 50, 75, 100, 300, 450, and 900
Important Notes
- Only whole numbers and integers can be converted to factors.
- Only composite numbers can have more than two factors.
- The smallest factor of a number is 1 and the biggest factor of a number would be the number itself.
Factors of 1000by Prime Factorization
Prime Factorization of 1000 refers to breaking down a number into the form of products of its prime factors. There are different methods that can be used to find the prime factorization of a number and its prime factors.
Method 1 - Division Method
To find the prime factors of 1000using the division method,
- Start dividing 1000from the smallest prime number i.e., 2, 3, 5, and so on,and find the smallest prime factor of the number.
- After finding the smallest prime factor of the number 1000, which is2,divide 1000by 2to obtain the quotient 500. Hence 500 and 2 are the factors of 1000.
- Repeat step 1with the obtained quotient (500) and continue until you reach quotient as 1.
So, the Prime factorization of 1000is 2× 2× 2× 5× 5× 5.
Method 2 -Factor Tree Method
We can do the same procedure used above, the factor tree as shown in the diagram given below:
Further, find the products of the multiplicands in different orders to obtain the composite factors of the number. Thus, the total factors of 1000including both theprime and composite numbers together can be written as, 1, 2, 4, 8, 10, 20, 25, 50, 100, 125, 200, 250, 500, 1000.
Factors of 1000 in Pairs
Pair factors are the pair of factors of anumberthat give the original number when multiplied together. The pair factors of 1000would be the two numbers when multiplied together, result in the value 1000.
The following table represents the calculation of pair factors of 1000:
| Pair Factorization | Factor Pair |
|---|---|
| 1× 1000 = 1000 | (1, 1000) |
| 2× 500 = 1000 | (2, 500) |
| 4 × 250 = 1000 | (4, 250) |
| 5 × 200 = 1000 | (5, 200) |
| 8 × 125 = 1000 | (8, 125) |
| 10× 100 = 1000 | (10, 100) |
| 20 ×50 = 1000 | (20, 50) |
| 25 × 40 = 1000 | (25, 40) |
Negative pair factors of 1000
The product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 104
The negative factor pairs of 104would be ( -1, -1000), ( -2, -500), ( -4, -250),( -5, -200), ( -8, -125), ( -10, -100), ( -20, -50) and ( -25, -40).
Solved Examples on factors of 1000
Example 1:Can you help Minnie calculate the sumof all the factors of 1000 that are also divisible by 10?
Solution
We know, the factors of 1000 also divisible by 10 are10, 20, 40, 50, 100, 200, 250, 500, and 1000.
Thus, the sum of all the factors of 1000 that are also divisible by 10 = 10 + 20 + 40 + 50 + 100 +200 +250 + 500 + 1000 = 2,170Example 2:What are the total positive pairs offactors of 1000?
Solution
We know, factors of 1000=1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500,1000
The factor pairs = (1, 1000), (2, 500), (4, 250), (5, 200), (8, 125), (10, 100), (20, 50), (25, 40)Hence, total factor pairs of 1000= 8
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FAQs onfactors of 1000
1. What are the factors of 1000?
The factors of 1000 are1 2,4,5, 8,10,20,25,40,50,100,125, 200,250, 500,and 1000.
2. Is 1000 a perfect square?
We know, 1000 = 2×2×2 ×5×5 ×5. Using prime factorization, we see that the square root of 1000 cannot be calculated.
Thus, 1000 is not a perfect square.
3. What number is a multiple and factor of 1000?
We know, Factors of 1000 = 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500,1000
Multiples of 1000 = 1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, and so on.
So, the only number that is both the factor and multiple of 1000 is 1000 itself.
4. What is the prime factorization of 1000?
Prime Factorization of a number refers to breaking down a number into the form of products of its prime factors.
So, the Prime factorization of 1000 is 23×53.
