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Factors of 1012

Factors of 1012 are the list of integers that can be evenly divided into 1012. There are overall 12 factors of 1012 among which 1012 is the biggest factor and 2, 11, 23 are its prime factors. The sum of all factors of 1012 is 2016.

All Factors of 1012: 1, 2, 4, 11, 22, 23, 44, 46, 92, 253, 506 and 1012
Prime Factors of 1012: 2, 11, 23
Prime Factorization of 1012: 2² × 11¹ × 23¹
Sum of Factors of 1012: 2016

1.	What Are the Factors of 1012?
2.	Factors of 1012 by Prime Factorization
3.	Factors of 1012 in Pairs
4.	FAQs on Factors of 1012

What are Factors of 1012?

Factors of 1012 are pairs of those numbers whose products result in 1012. These factors are either prime numbers or composite numbers.

How to Find the Factors of 1012?

To find the factors of 1012, we will have to find the list of numbers that would divide 1012 without leaving any remainder.

1012/2 = 506; therefore, 2 is a factor of 1012 and 506 is also a factor of 1012.
1012/92 = 11; therefore, 92 is a factor of 1012 and 11 is also a factor of 1012.

Similarly we can find other factors. Hence, the factors of 1012 are 1, 2, 4, 11, 22, 23, 44, 46, 92, 253, 506, 1012.

☛ Also Check:

Factors of 98 - The factors of 98 are 1, 2, 7, 14, 49, 98
Factors of 65 - The factors of 65 are 1, 5, 13, 65
Factors of 121 - The factors of 121 are 1, 11, 121
Factors of 6 - The factors of 6 are 1, 2, 3, 6
Factors of 33 - The factors of 33 are 1, 3, 11, 33

Factors of 1012 by Prime Factorization

The number 1012 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 1012. The first step is to divide the number 1012 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.

1012 ÷ 2 = 506
506 ÷ 2 = 253

Further dividing 253 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 253 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 1012 can be written as 2² × 11¹ × 23¹ where 2, 11, 23 are prime.

Factors of 1012 in Pairs

Pair factors of 1012 are the pairs of numbers that when multiplied give the product 1012. The factors of 1012 in pairs are:

1 × 1012 = (1, 1012)
2 × 506 = (2, 506)
4 × 253 = (4, 253)
11 × 92 = (11, 92)
22 × 46 = (22, 46)
23 × 44 = (23, 44)

Negative pair factors of 1012 are:

-1 × -1012 = (-1, -1012)
-2 × -506 = (-2, -506)
-4 × -253 = (-4, -253)
-11 × -92 = (-11, -92)
-22 × -46 = (-22, -46)
-23 × -44 = (-23, -44)

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

Factors of 1012 Solved Examples

Example 1: How many factors are there for 1012?

Solution:

The factors of 1012 are too many, therefore if we can find the prime factorization of 1012, 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 1012 = 2² × 11¹ × 23¹
Therefore, the total number of factors are (2 + 1) × (1 + 1) × (1 + 1) = 3 × 2 × 2 = 12
Example 2: Find the Least Common Multiple and Highest Common Factor (HCF) of 1012 and 75.

Solution:

The factors of 1012 are 1, 2, 4, 11, 22, 23, 44, 46, 92, 253, 506, 1012 and factors of 75 are 1, 3, 5, 15, 25, 75.

Therefore, the Least Common Multiple of 1012 and 75 is 75900 and Highest Common Factor (HCF) of 1012 and 75 is 1.
Example 3: Find if 2, 4, 23, 44, 92, 596 and 1012 are factors of 1012.

Solution:

When we divide 1012 by 596 it leaves a remainder. Therefore, the number 596 is not a factor of 1012. All numbers except 596 are factors of 1012.
Example 4: Find the product of all the prime factors of 1012.

Solution:

Since, the prime factors of 1012 are 2, 11, 23. Therefore, the product of prime factors = 2 × 11 × 23 = 506.

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FAQs on Factors of 1012

What are the Factors of 1012?

The factors of 1012 are 1, 2, 4, 11, 22, 23, 44, 46, 92, 253, 506, 1012 and its negative factors are -1, -2, -4, -11, -22, -23, -44, -46, -92, -253, -506, -1012.

What is the Sum of Factors of 1012?

Sum of all factors of 1012 = (2^{2 + 1} - 1)/(2 - 1) × (11^{1 + 1} - 1)/(11 - 1) × (23^{1 + 1} - 1)/(23 - 1) = 2016

What numbers are the Pair Factors of 1012?

The pair factors of 1012 are (1, 1012), (2, 506), (4, 253), (11, 92), (22, 46), (23, 44).

What is the Greatest Common Factor of 1012 and 34?

The factors of 1012 and 34 are 1, 2, 4, 11, 22, 23, 44, 46, 92, 253, 506, 1012 and 1, 2, 17, 34 respectively.

Common factors of 1012 and 34 are [1, 2].

Hence, the GCF of 1012 and 34 is 2.

How Many Factors of 1012 are also common to the Factors of 642?

Since, the factors of 1012 are 1, 2, 4, 11, 22, 23, 44, 46, 92, 253, 506, 1012 and the factors of 642 are 1, 2, 3, 6, 107, 214, 321, 642.
Hence, [1, 2] are the common factors of 1012 and 642.

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