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Factors of 990

Factors of 990 are the list of integers that we can split evenly into 990. It has total 24 factors of which 990 is the biggest factor and the prime factors of 990 are 2, 3, 5, 11. The sum of all factors of 990 is 2808.

All Factors of 990: 1, 2, 3, 5, 6, 9, 10, 11, 15, 18, 22, 30, 33, 45, 55, 66, 90, 99, 110, 165, 198, 330, 495 and 990
Prime Factors of 990: 2, 3, 5, 11
Prime Factorization of 990: 2¹ × 3² × 5¹ × 11¹
Sum of Factors of 990: 2808

1.	What Are the Factors of 990?
2.	Factors of 990 by Prime Factorization
3.	Factors of 990 in Pairs
4.	FAQs on Factors of 990

What are Factors of 990?

Factors of 990 are pairs of those numbers whose products result in 990. These factors are either prime numbers or composite numbers.

How to Find the Factors of 990?

To find the factors of 990, we will have to find the list of numbers that would divide 990 without leaving any remainder.

990/18 = 55; therefore, 18 is a factor of 990 and 55 is also a factor of 990.
990/198 = 5; therefore, 198 is a factor of 990 and 5 is also a factor of 990.

Similarly we can find other factors. Hence, the factors of 990 are 1, 2, 3, 5, 6, 9, 10, 11, 15, 18, 22, 30, 33, 45, 55, 66, 90, 99, 110, 165, 198, 330, 495, 990.

☛ Also Check:

Factors of 121 - The factors of 121 are 1, 11, 121
Factors of 21 - The factors of 21 are 1, 3, 7, 21
Factors of 65 - The factors of 65 are 1, 5, 13, 65
Factors of 80 - The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
Factors of 55 - The factors of 55 are 1, 5, 11, 55

Factors of 990 by Prime Factorization

The number 990 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 990. The first step is to divide the number 990 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.

990 ÷ 2 = 495

Further dividing 495 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 495 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 990 can be written as 2¹ × 3² × 5¹ × 11¹ where 2, 3, 5, 11 are prime.

Factors of 990 in Pairs

Pair factors of 990 are the pairs of numbers that when multiplied give the product 990. The factors of 990 in pairs are:

1 × 990 = (1, 990)
2 × 495 = (2, 495)
3 × 330 = (3, 330)
5 × 198 = (5, 198)
6 × 165 = (6, 165)
9 × 110 = (9, 110)
10 × 99 = (10, 99)
11 × 90 = (11, 90)
15 × 66 = (15, 66)
18 × 55 = (18, 55)
22 × 45 = (22, 45)
30 × 33 = (30, 33)

Negative pair factors of 990 are:

-1 × -990 = (-1, -990)
-2 × -495 = (-2, -495)
-3 × -330 = (-3, -330)
-5 × -198 = (-5, -198)
-6 × -165 = (-6, -165)
-9 × -110 = (-9, -110)
-10 × -99 = (-10, -99)
-11 × -90 = (-11, -90)
-15 × -66 = (-15, -66)
-18 × -55 = (-18, -55)
-22 × -45 = (-22, -45)
-30 × -33 = (-30, -33)

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

Factors of 990 Solved Examples

Example 1: How many factors are there for 990?

Solution:

The factors of 990 are too many, therefore if we can find the prime factorization of 990, 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 990 = 2¹ × 3² × 5¹ × 11¹
Therefore, the total number of factors are (1 + 1) × (2 + 1) × (1 + 1) × (1 + 1) = 2 × 3 × 2 × 2 = 24
Example 2: Find the Lowest Common Multiple (LCM) and Greatest Common Divisor (GCD) of 990 and 691.

Solution:

The factors of 990 are 1, 2, 3, 5, 6, 9, 10, 11, 15, 18, 22, 30, 33, 45, 55, 66, 90, 99, 110, 165, 198, 330, 495, 990 and factors of 691 are 1, 691.

Therefore, the Lowest Common Multiple (LCM) of 990 and 691 is 684090 and Greatest Common Divisor (GCD) of 990 and 691 is 1.
Example 3: Find if 2, 3, 9, 10, 30, 33, 45 and 554 are factors of 990.

Solution:

When we divide 990 by 554 it leaves a remainder. Therefore, the number 554 is not a factor of 990. All numbers except 554 are factors of 990.
Example 4: Find the product of all the prime factors of 990.

Solution:

Since, the prime factors of 990 are 2, 3, 5, 11. Therefore, the product of prime factors = 2 × 3 × 5 × 11 = 330.

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FAQs on Factors of 990

What are the Factors of 990?

The factors of 990 are 1, 2, 3, 5, 6, 9, 10, 11, 15, 18, 22, 30, 33, 45, 55, 66, 90, 99, 110, 165, 198, 330, 495, 990 and its negative factors are -1, -2, -3, -5, -6, -9, -10, -11, -15, -18, -22, -30, -33, -45, -55, -66, -90, -99, -110, -165, -198, -330, -495, -990.

What is the Sum of the Factors of 990?

Sum of all factors of 990 = (2^{1 + 1} - 1)/(2 - 1) × (3^{2 + 1} - 1)/(3 - 1) × (5^{1 + 1} - 1)/(5 - 1) × (11^{1 + 1} - 1)/(11 - 1) = 2808

What are the Pair Factors of 990?

The pair factors of 990 are (1, 990), (2, 495), (3, 330), (5, 198), (6, 165), (9, 110), (10, 99), (11, 90), (15, 66), (18, 55), (22, 45), (30, 33).

What is the Greatest Common Factor of 990 and 443?

The factors of 990 are 1, 2, 3, 5, 6, 9, 10, 11, 15, 18, 22, 30, 33, 45, 55, 66, 90, 99, 110, 165, 198, 330, 495, 990 and the factors of 443 are 1, 443. 990 and 443 have only one common factor which is 1. This implies that 990 and 443 are co-prime.

Hence, the Greatest Common Factor (GCF) of 990 and 443 is 1.

How Many Factors of 134 are also common to the Factors of 990?

Since, the factors of 990 are 1, 2, 3, 5, 6, 9, 10, 11, 15, 18, 22, 30, 33, 45, 55, 66, 90, 99, 110, 165, 198, 330, 495, 990 and the factors of 134 are 1, 2, 67, 134.
Hence, [1, 2] are the common factors of 990 and 134.

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