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Factors of 1001

Factors of 1001 are numbers that, when multiplied in pairs give the product as 1001. There are overall 8 factors of 1001 i.e. 1, 7, 11, 13, 77, 91, 143, 1001 where 1001 is the biggest factor. The sum of all factors of 1001 is 1344. Its Prime Factors are 7 × 11 × 13 and (1, 1001), (7, 143), (11, 91), (13, 77) are Pair Factors.

All Factors of 1001: 1, 7, 11, 13, 77, 91, 143 and 1001
Negative Factors of 1001: -1, -7, -11, -13, -77, -91, -143 and -1001
Prime Factors of 1001: 7, 11, 13
Prime Factorization of 1001: 7¹ × 11¹ × 13¹
Sum of Factors of 1001: 1344

1.	What Are the Factors of 1001?
2.	Factors of 1001 by Prime Factorization
3.	Factors of 1001 in Pairs
4.	FAQs on Factors of 1001

What are Factors of 1001?

Factors of 1001 are pairs of those numbers whose products result in 1001. These factors are either prime numbers or composite numbers.

How to Find the Factors of 1001?

To find the factors of 1001, we will have to find the list of numbers that would divide 1001 without leaving any remainder.

1001/7 = 143; therefore, 7 is a factor of 1001 and 143 is also a factor of 1001.
1001/13 = 77; therefore, 13 is a factor of 1001 and 77 is also a factor of 1001.

Similarly we can find other factors. Hence, the factors of 1001 are 1, 7, 11, 13, 77, 91, 143, 1001.

☛ Also Check:

Factors of 63 - The factors of 63 are 1, 3, 7, 9, 21, 63
Factors of 39 - The factors of 39 are 1, 3, 13, 39
Factors of 27 - The factors of 27 are 1, 3, 9, 27
Factors of 96 - The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
Factors of 55 - The factors of 55 are 1, 5, 11, 55

Factors of 1001 by Prime Factorization

The number 1001 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 1001. The first step is to divide the number 1001 with the smallest prime factor, here it is 7. We keep dividing until it gives a non-zero remainder.

1001 ÷ 7 = 143

Further dividing 143 by 7 gives a non-zero remainder. So we stop the process and continue dividing the number 143 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 1001 can be written as 7¹ × 11¹ × 13¹ where 7, 11, 13 are prime.

Factors of 1001 in Pairs

Pair factors of 1001 are the pairs of numbers that when multiplied give the product 1001. The factors of 1001 in pairs are:

1 × 1001 = (1, 1001)
7 × 143 = (7, 143)
11 × 91 = (11, 91)
13 × 77 = (13, 77)

Negative pair factors of 1001 are:

-1 × -1001 = (-1, -1001)
-7 × -143 = (-7, -143)
-11 × -91 = (-11, -91)
-13 × -77 = (-13, -77)

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

Factors of 1001 Solved Examples

Example 1: How many factors are there for 1001?

Solution:

The factors of 1001 are 1, 7, 11, 13, 77, 91, 143, 1001. Therefore, 1001 has 8 factors.
Example 2: Find the Least Common Multiple and Greatest Common Divisor (GCD) of 1001 and 860.

Solution:

The factors of 1001 are 1, 7, 11, 13, 77, 91, 143, 1001 and factors of 860 are 1, 2, 4, 5, 10, 20, 43, 86, 172, 215, 430, 860.

Therefore, the Least Common Multiple of 1001 and 860 is 860860 and Greatest Common Divisor (GCD) of 1001 and 860 is 1.
Example 3: Find if 1, 13, 91, 694 and 1001 are factors of 1001.

Solution:

When we divide 1001 by 694 it leaves a remainder. Therefore, the number 694 is not a factor of 1001. All numbers except 694 are factors of 1001.
Example 4: Find the product of all the prime factors of 1001.

Solution:

Since, the prime factors of 1001 are 7, 11, 13. Therefore, the product of prime factors = 7 × 11 × 13 = 1001.

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FAQs on Factors of 1001

What are the Factors of 1001?

The factors of 1001 are 1, 7, 11, 13, 77, 91, 143, 1001 and its negative factors are -1, -7, -11, -13, -77, -91, -143, -1001.

What is the Sum of all Factors of 1001?

Sum of all factors of 1001 = (7^{1 + 1} - 1)/(7 - 1) × (11^{1 + 1} - 1)/(11 - 1) × (13^{1 + 1} - 1)/(13 - 1) = 1344

What are the Pair Factors of 1001?

The pair factors of 1001 are (1, 1001), (7, 143), (11, 91), (13, 77).

What is the Greatest Common Factor of 1001 and 822?

The factors of 1001 are 1, 7, 11, 13, 77, 91, 143, 1001 and the factors of 822 are 1, 2, 3, 6, 137, 274, 411, 822. 1001 and 822 have only one common factor which is 1. This implies that 1001 and 822 are co-prime.

Hence, the Greatest Common Factor (GCF) of 1001 and 822 is 1.

How Many Factors of 1001 are also Factors of 851?

Since, the factors of 1001 are 1, 7, 11, 13, 77, 91, 143, 1001 and factors of 851 are 1, 23, 37, 851. Hence, 1001 and 851 have only one common factor which is 1. Therefore, 1001 and 851 are co-prime.

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