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Factors of 960

Factors of 960 are the list of integers that we can split evenly into 960. There are 28 factors of 960, of which the following are its prime factors 2, 3, 5. The sum of all factors of 960 is 3048.

All Factors of 960: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480 and 960
Prime Factors of 960: 2, 3, 5
Prime Factorization of 960: 2⁶ × 3¹ × 5¹
Sum of Factors of 960: 3048

1.	What Are the Factors of 960?
2.	Factors of 960 by Prime Factorization
3.	Factors of 960 in Pairs
4.	FAQs on Factors of 960

What are Factors of 960?

Factors of 960 are pairs of those numbers whose products result in 960. These factors are either prime numbers or composite numbers.

How to Find the Factors of 960?

To find the factors of 960, we will have to find the list of numbers that would divide 960 without leaving any remainder.

960/2 = 480; therefore, 2 is a factor of 960 and 480 is also a factor of 960.
960/5 = 192; therefore, 5 is a factor of 960 and 192 is also a factor of 960.

Similarly we can find other factors. Hence, the factors of 960 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960.

☛ Also Check:

Factors of 29 - The factors of 29 are 1, 29
Factors of 55 - The factors of 55 are 1, 5, 11, 55
Factors of 23 - The factors of 23 are 1, 23
Factors of 34 - The factors of 34 are 1, 2, 17, 34
Factors of 25 - The factors of 25 are 1, 5, 25

Factors of 960 by Prime Factorization

The number 960 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 960. The first step is to divide the number 960 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.

960 ÷ 2 = 480
480 ÷ 2 = 240
240 ÷ 2 = 120
120 ÷ 2 = 60
60 ÷ 2 = 30
30 ÷ 2 = 15

Further dividing 15 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 15 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 960 can be written as 2⁶ × 3¹ × 5¹ where 2, 3, 5 are prime.

Factors of 960 in Pairs

Pair factors of 960 are the pairs of numbers that when multiplied give the product 960. The factors of 960 in pairs are:

1 × 960 = (1, 960)
2 × 480 = (2, 480)
3 × 320 = (3, 320)
4 × 240 = (4, 240)
5 × 192 = (5, 192)
6 × 160 = (6, 160)
8 × 120 = (8, 120)
10 × 96 = (10, 96)
12 × 80 = (12, 80)
15 × 64 = (15, 64)
16 × 60 = (16, 60)
20 × 48 = (20, 48)
24 × 40 = (24, 40)
30 × 32 = (30, 32)

Negative pair factors of 960 are:

-1 × -960 = (-1, -960)
-2 × -480 = (-2, -480)
-3 × -320 = (-3, -320)
-4 × -240 = (-4, -240)
-5 × -192 = (-5, -192)
-6 × -160 = (-6, -160)
-8 × -120 = (-8, -120)
-10 × -96 = (-10, -96)
-12 × -80 = (-12, -80)
-15 × -64 = (-15, -64)
-16 × -60 = (-16, -60)
-20 × -48 = (-20, -48)
-24 × -40 = (-24, -40)
-30 × -32 = (-30, -32)

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

Factors of 960 Solved Examples

Example 1: How many factors are there for 960?

Solution:

The factors of 960 are too many, therefore if we can find the prime factorization of 960, 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 960 = 2⁶ × 3¹ × 5¹
Therefore, the total number of factors are (6 + 1) × (1 + 1) × (1 + 1) = 7 × 2 × 2 = 28
Example 2: Find the Least Common Multiple (LCM) and Greatest Common Divisor (GCD) of 960 and 94.

Solution:

The factors of 960 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960 and factors of 94 are 1, 2, 47, 94.

Therefore, the Least Common Multiple (LCM) of 960 and 94 is 45120 and Greatest Common Divisor (GCD) of 960 and 94 is 2.
Example 3: Find if 3, 30, 32, 60, 64, 80, 152 and 960 are factors of 960.

Solution:

When we divide 960 by 152 it leaves a remainder. Therefore, the number 152 is not a factor of 960. All numbers except 152 are factors of 960.
Example 4: Find the product of all the prime factors of 960.

Solution:

Since, the prime factors of 960 are 2, 3, 5. Therefore, the product of prime factors = 2 × 3 × 5 = 30.

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FAQs on Factors of 960

What are the Factors of 960?

The factors of 960 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960 and its negative factors are -1, -2, -3, -4, -5, -6, -8, -10, -12, -15, -16, -20, -24, -30, -32, -40, -48, -60, -64, -80, -96, -120, -160, -192, -240, -320, -480, -960.

What is the Sum of all the Factors of 960?

Sum of all factors of 960 = (2^{6 + 1} - 1)/(2 - 1) × (3^{1 + 1} - 1)/(3 - 1) × (5^{1 + 1} - 1)/(5 - 1) = 3048

What Numbers are the Prime Factors of 960?

The prime factors of 960 are 2, 3, 5.

What is the Greatest Common Factor of 960 and 524?

The factors of 960 and 524 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960 and 1, 2, 4, 131, 262, 524 respectively.

Common factors of 960 and 524 are [1, 2, 4].

Hence, the Greatest Common Factor of 960 and 524 is 4.

How Many Factors of 960 are also common to the Factors of 688?

Since, the factors of 960 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960 and the factors of 688 are 1, 2, 4, 8, 16, 43, 86, 172, 344, 688.
Hence, [1, 2, 4, 8, 16] are the common factors of 960 and 688.

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