Factors of 1001

Factors of 1001 are the numbers that can divide 1001 completely or evenly. If the product of any two whole numbers results in 1001, then they become the factors of 1001. Such pairs of numbers are the pair factors of 1001, such as (1, 1001), (7, 143), (11, 91), (13, 77). Since 1001 is a composite number, it will have more than two factors. There are a total of 8 factors of 1001, they are 1, 7, 11,13, 77, 91, 143 and 1001. The prime factorisation of 1001 results in 7 × 11 × 13.

What are Factors of 1001?

Integers that can divide 1001 exactly, are called factors of 1001. Hence, after division, there shall be no remainder left and so, a fraction cannot be a factor of 1001. These factors can be a prime number or a composite number. The smallest factor is 1 and the largest factor of 1001 is 1001 itself.

Another definition of factors of 1001 that we can give, is the pair of numbers that results in 1001 when multiplied by each other. Now let us learn how to find these factors.

How to Find Factors of 1001?

There are two ways we can find the factors of 1001, either dividing 1001 by a list of numbers that can divide it completely or finding any two natural numbers whose product is equal to 1001.

Let us proceed with the division method.

• 1001 ÷ 1 = 1001
• 1001 ÷ 7 = 143
• 1001 ÷ 11 = 91
• 1001 ÷ 13 = 77
• 1001 ÷ 77 = 13
• 1001 ÷ 91 = 11
• 1001 ÷ 143 = 7
• 1001 ÷ 1001 = 1

Therefore, the factors of 1001 are 1, 7, 11,13, 77, 91, 143 and 1001.

Pair Factors of 1001

Pair factors of 1001 are those integers that result in the original number when multiplied in pairs. Suppose 1001 multiplied by 1 is equal to 1001, then (1001, 1) is a pair factor of 1001. Hence, we can write the factors of 1001 in pairs as:

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

Since a product of two negative numbers results in a positive value, we can consider the negative pairs factors of 1001, too.

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

Note: A pair factor of 1001 will have the same sign always.

Prime Factorisation of 1001

We can evaluate the prime factors of 1001 using the factorisation method. Prime factors are the prime numbers that can divide 1001, uniformly. Now to find these prime factors, we have to divide by prime numbers only, starting from the smallest to the largest. Let us take the steps one by one.

Step 1: 1001 is divisible by the smallest prime factor, i.e., 7, hence, 1001 ÷ 7 = 143

Step 2: 143 is not divisible by 7 but it is divisible by the next smallest prime factor, i.e. Hence, 143 ÷ 11 = 13

Step 3: Now, 13 is itself a prime number, therefore divisible by itself. 13 ÷ 13 = 1

Hence, the prime factorisation of 1001 is 7¹ × 11¹ × 13¹ and the prime factors of 1001 are 7, 11 and 13.

Video Lesson on Prime Factors

Factor Tree of 1001

Related Articles

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• Factors Of 120
• Factors of 144
• Factors of 150
• Factors of 215
• Factors of 216

Solved Examples

Q.1: How many factors of 1001 are odd numbers?

Solution: As we know, the factors of 1001 are 1, 7, 11, 13, 77, 91, 143, 1001. By definition, odd numbers are the numbers that are divisible by 2 completely. So, all the factors of 1001 are not divisible by 2. Hence, there are 8 odd factors of 1001.

Q.2: What are the common factors between 1001 and 101?

Solution: The factors of 101 are 1, 101.

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

Therefore, the common factor between 1001 and 101 is 1.

Q.3: Find the Highest Common Factor of 1001 and 5005?

Solution: If we find HCF of 1001 and 5005, by division method, then we get;

HCF (1001, 5005) = 1001

Clearly,

1001 x 5 = 5005

Thus, 1001 is the GCF of 1001 and 5005.