Factors of 90

Factors of 90 are integers that can be divided evenly into 90. There are 12 factors of 90 of which 90 itself is the biggest factor and its prime factors are 2, 3, and 5 The Prime Factorization of 90 is 2 × 3² × 5.

• Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45 and 90
• Negative Factors of 90: -1, -2, -3, -5, -6, -9, -10, -15, -18, -30, -45 and -90
• Prime Factors of 90: 2, 3, 5
• Prime Factorization of 90: 2 × 3 × 3 × 5 = 2 × 3² × 5
• Sum of Factors of 90: 234

What are the Factors of 90?

A factor is a number that divides another number without leaving any remainder. When we divide 90 by 3 it is exactly divisible and leaves no remainder. Therefore, 3 is a factor of 90. Similarly, if we divide 90 by 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90, they are exactly divisible and leave no reminder. Note that 1 and the number itself are always factors of the number. Therefore, the factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90

How to Calculate the Factors of 90?

The division method can be used to find the factors of 90. In the division method, we find the numbers which divide 90 exactly without leaving a remainder.

Factors of 90 by Division Method

We should divide 90 by natural numbers and see which all numbers exactly divide 90 and bring 0 as a reminder for getting the factors of 90. Let us try dividing 90 by 2, 3, 5, 9, and see if they are exactly divisible. They are divisible so they are factors of 90. Similarly, 10, 15, 18, 30, 45, and 90 are also factors of 90. Just try dividing 90 by using the above numbers. At the same time, if we take numbers like 4, 7, and 8 in a random way, we can see that they are not exactly divisible. Now, we can have 4, 7, and 8 leaves remainders. So they are not factors of 90

Explore factors using illustrations and interactive examples.

• Factors of 69: The factors of 69 are 1, 3, 23, 69.
• Factors of 49 - The factors of 49 are 1, 7, 49
• Factors of 96 - The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
• Factors of 119 - The factors of 119 are 1, 7, 17, 119
• Factors of 91 - The factors of 91 are 1, 7 13, 91
• Factors of 900 - The factors of 900 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450

Factors of 90 by Prime Factorization

Dividing number 90 by prime numbers and seeing if it does not leave any remainder and continuing the division with the quotient is called the prime factorization method. Then we express 90 as a product of its prime factors. We can find the prime factors by the division method or factor tree method.

1. Prime Factorization of 90 by Division Method

90 is divided by the smallest prime number which divides 90 exactly. The quotient thus obtained is then divided by the smallest or second smallest prime number and the process continues till the quotient is not dividable. Let us divide 90 by the prime number 3

• 90 ÷ 3 = 30

Here 30 is a composite number that can further be divided by 3

• 30 ÷ 3 = 10

Again 10 is a composite number that can be further divided by 2

• 10 ÷ 2 = 5

Since 5 is an odd prime number, it cannot be further divided. Therefore the prime factorization of 90 is 90 =3 × 3 × 5 × 2. Taking another prime number which is a factor of 90. Let us divide 90 by the number 2 (even prime number).

• 90 ÷ 2= 45

45 is a composite number, so it can be further divided by 5

• 45 ÷ 5 = 9

Again 9 is further divided by 3

• 9 ÷ 3 = 3

Now, 3 is a prime number that cannot be divided further. Therefore the prime factorization of 90 is 90 =3 × 3 × 5 × 2. Interesting right! Now, try the division method of prime factorization of 90 by another prime number 5

2. Prime Factorization by Factor Tree Method

We have to find the prime factors of 90, therefore the root of our factor tree is 90. Pair factors of 90 have to be written as its branches. Here let us take the prime number 5 to divide 90 in the factor tree method.

3 is a prime number, so ends the factor tree. Therefore prime factorization of 90 is 5 × 2 × 3 ×3. Similarly, you can also try the factor tree method with other prime numbers 2 and 3

3. Prime Factorization of 90 by Upside Down Division Method

This method is called the upside-down division method because the division symbol is flipped upside down. Here we divide 90 by the prime number 3

5 is a prime number, it cannot be further divided. Therefore prime factorization of 90 is 3 × 3 × 5 × 2. You can try this upside-down method by other prime factors of 90 such as 2 and 3

The set of two numbers when multiplied will get a product is called pair factors. Pair factors of 90 are

• 1 × 90 = 90
• 2 × 45 = 90
• 3 × 30 = 90
• 5 × 18  = 90
• 6 × 15  = 90
• 9 × 10  = 90
• The factors of 90 in pairs are (1, 90), (2, 45), (3, 30), (5, 18), (6, 15) and (9, 10)
• There can be negative pair factors also ( -1, -90), (-2, -45), (-3, -30), (-5, -18), (-6, -15) and (-9, -10)

Important Notes:

• Factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90
• There are negative pair factors of 90
• Prime factorization can be done by the division method, factor tree method, and upside down division method.