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Factors of 2010

Factors of 2010 are the list of integers that can be evenly divided into 2010. There are overall 16 factors of 2010 among which 2010 is the biggest factor and 2, 3, 5, 67 are its prime factors. The Prime Factorization of 2010 is 2¹ × 3¹ × 5¹ × 67¹.

All Factors of 2010: 1, 2, 3, 5, 6, 10, 15, 30, 67, 134, 201, 335, 402, 670, 1005 and 2010
Prime Factors of 2010: 2, 3, 5, 67
Prime Factorization of 2010: 2¹ × 3¹ × 5¹ × 67¹
Sum of Factors of 2010: 4896

1.	What Are the Factors of 2010?
2.	Factors of 2010 by Prime Factorization
3.	Factors of 2010 in Pairs
4.	FAQs on Factors of 2010

What are Factors of 2010?

Factors of 2010 are pairs of those numbers whose products result in 2010. These factors are either prime numbers or composite numbers.

How to Find the Factors of 2010?

To find the factors of 2010, we will have to find the list of numbers that would divide 2010 without leaving any remainder.

2010/402 = 5; therefore, 402 is a factor of 2010 and 5 is also a factor of 2010.
2010/1005 = 2; therefore, 1005 is a factor of 2010 and 2 is also a factor of 2010.

Similarly we can find other factors. Hence, the factors of 2010 are 1, 2, 3, 5, 6, 10, 15, 30, 67, 134, 201, 335, 402, 670, 1005, 2010.

☛ Also Check:

Factors of 96 - The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
Factors of 17 - The factors of 17 are 1, 17
Factors of 98 - The factors of 98 are 1, 2, 7, 14, 49, 98
Factors of 33 - The factors of 33 are 1, 3, 11, 33
Factors of 91 - The factors of 91 are 1, 7, 13, 91

Factors of 2010 by Prime Factorization

The number 2010 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 2010. The first step is to divide the number 2010 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.

2010 ÷ 2 = 1005

Further dividing 1005 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 1005 by the next smallest prime factor. We stop ultimately if the next prime factor doesn't exist or when we can't divide any further.

So, the prime factorization of 2010 can be written as 2¹ × 3¹ × 5¹ × 67¹ where 2, 3, 5, 67 are prime.

Factors of 2010 in Pairs

Pair factors of 2010 are the pairs of numbers that when multiplied give the product 2010. The factors of 2010 in pairs are:

1 × 2010 = (1, 2010)
2 × 1005 = (2, 1005)
3 × 670 = (3, 670)
5 × 402 = (5, 402)
6 × 335 = (6, 335)
10 × 201 = (10, 201)
15 × 134 = (15, 134)
30 × 67 = (30, 67)

Negative pair factors of 2010 are:

-1 × -2010 = (-1, -2010)
-2 × -1005 = (-2, -1005)
-3 × -670 = (-3, -670)
-5 × -402 = (-5, -402)
-6 × -335 = (-6, -335)
-10 × -201 = (-10, -201)
-15 × -134 = (-15, -134)
-30 × -67 = (-30, -67)

NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.

Factors of 2010 Solved Examples

Example 1: How many factors are there for 2010?

Solution:

The factors of 2010 are too many, therefore if we can find the prime factorization of 2010, then the total number of factors can be calculated using the formula shown below.
If the prime factorization of the number is a^x × b^y × c^z where a, b, c are prime, then the total number of factors can be given by (x + 1)(y + 1)(z + 1).

Prime Factorization of 2010 = 2¹ × 3¹ × 5¹ × 67¹
Therefore, the total number of factors are (1 + 1) × (1 + 1) × (1 + 1) × (1 + 1) = 2 × 2 × 2 × 2 = 16
Example 2: Find the Least Common Multiple (LCM) and Greatest Common Factor (GCF) of 2010 and 1123.

Solution:

The factors of 2010 are 1, 2, 3, 5, 6, 10, 15, 30, 67, 134, 201, 335, 402, 670, 1005, 2010 and factors of 1123 are 1, 1123.

Therefore, the Least Common Multiple (LCM) of 2010 and 1123 is 2257230 and Greatest Common Factor (GCF) of 2010 and 1123 is 1.
Example 3: Find if 1, 3, 5, 134, 335, 529, 1005 and 2010 are factors of 2010.

Solution:

When we divide 2010 by 529 it leaves a remainder. Therefore, the number 529 is not a factor of 2010. All numbers except 529 are factors of 2010.
Example 4: Find the product of all the prime factors of 2010.

Solution:

Since, the prime factors of 2010 are 2, 3, 5, 67. Therefore, the product of prime factors = 2 × 3 × 5 × 67 = 2010.

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FAQs on Factors of 2010

What are the Factors of 2010?

The factors of 2010 are 1, 2, 3, 5, 6, 10, 15, 30, 67, 134, 201, 335, 402, 670, 1005, 2010 and its negative factors are -1, -2, -3, -5, -6, -10, -15, -30, -67, -134, -201, -335, -402, -670, -1005, -2010.

What is the Sum of all Factors of 2010?

Sum of all factors of 2010 = (2^{1 + 1} - 1)/(2 - 1) × (3^{1 + 1} - 1)/(3 - 1) × (5^{1 + 1} - 1)/(5 - 1) × (67^{1 + 1} - 1)/(67 - 1) = 4896

What are the Pair Factors of 2010?

The pair factors of 2010 are (1, 2010), (2, 1005), (3, 670), (5, 402), (6, 335), (10, 201), (15, 134), (30, 67).

What is the Greatest Common Factor of 2010 and 1530?

The factors of 2010 and 1530 are 1, 2, 3, 5, 6, 10, 15, 30, 67, 134, 201, 335, 402, 670, 1005, 2010 and 1, 2, 3, 5, 6, 9, 10, 15, 17, 18, 30, 34, 45, 51, 85, 90, 102, 153, 170, 255, 306, 510, 765, 1530 respectively.

Common factors of 2010 and 1530 are [1, 2, 3, 5, 6, 10, 15, 30].

Hence, the Greatest Common Factor (GCF) of 2010 and 1530 is 30.

How Many Factors of 2010 are also Factors of 1242?

Since, the factors of 2010 are 1, 2, 3, 5, 6, 10, 15, 30, 67, 134, 201, 335, 402, 670, 1005, 2010 and the factors of 1242 are 1, 2, 3, 6, 9, 18, 23, 27, 46, 54, 69, 138, 207, 414, 621, 1242.
Hence, [1, 2, 3, 6] are the common factors of 2010 and 1242.

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