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Factors of 1280

Factors of 1280 are numbers that, when multiplied in pairs give the product as 1280. There are overall 18 factors of 1280 among which 1280 is the biggest factor and 2, 5 are its prime factors. The sum of all factors of 1280 is 3066.

All Factors of 1280: 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 256, 320, 640 and 1280
Prime Factors of 1280: 2, 5
Prime Factorization of 1280: 2⁸ × 5¹
Sum of Factors of 1280: 3066

1.	What Are the Factors of 1280?
2.	Factors of 1280 by Prime Factorization
3.	Factors of 1280 in Pairs
4.	FAQs on Factors of 1280

What are Factors of 1280?

Factors of 1280 are pairs of those numbers whose products result in 1280. These factors are either prime numbers or composite numbers.

How to Find the Factors of 1280?

To find the factors of 1280, we will have to find the list of numbers that would divide 1280 without leaving any remainder.

1280/160 = 8; therefore, 160 is a factor of 1280 and 8 is also a factor of 1280.
1280/10 = 128; therefore, 10 is a factor of 1280 and 128 is also a factor of 1280.

Similarly we can find other factors. Hence, the factors of 1280 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 256, 320, 640, 1280.

☛ Also Check:

Factors of 40 - The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40
Factors of 20 - The factors of 20 are 1, 2, 4, 5, 10, 20
Factors of 63 - The factors of 63 are 1, 3, 7, 9, 21, 63
Factors of 70 - The factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70
Factors of 39 - The factors of 39 are 1, 3, 13, 39

Factors of 1280 by Prime Factorization

The number 1280 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 1280. The first step is to divide the number 1280 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.

1280 ÷ 2 = 640
640 ÷ 2 = 320
320 ÷ 2 = 160
160 ÷ 2 = 80
80 ÷ 2 = 40
40 ÷ 2 = 20
20 ÷ 2 = 10
10 ÷ 2 = 5

Further dividing 5 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 5 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 1280 can be written as 2⁸ × 5¹ where 2, 5 are prime.

Factors of 1280 in Pairs

Pair factors of 1280 are the pairs of numbers that when multiplied give the product 1280. The factors of 1280 in pairs are:

1 × 1280 = (1, 1280)
2 × 640 = (2, 640)
4 × 320 = (4, 320)
5 × 256 = (5, 256)
8 × 160 = (8, 160)
10 × 128 = (10, 128)
16 × 80 = (16, 80)
20 × 64 = (20, 64)
32 × 40 = (32, 40)

Negative pair factors of 1280 are:

-1 × -1280 = (-1, -1280)
-2 × -640 = (-2, -640)
-4 × -320 = (-4, -320)
-5 × -256 = (-5, -256)
-8 × -160 = (-8, -160)
-10 × -128 = (-10, -128)
-16 × -80 = (-16, -80)
-20 × -64 = (-20, -64)
-32 × -40 = (-32, -40)

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

Factors of 1280 Solved Examples

Example 1: How many factors are there for 1280?

Solution:

The factors of 1280 are too many, therefore if we can find the prime factorization of 1280, 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 1280 = 2⁸ × 5¹
Therefore, the total number of factors are (8 + 1) × (1 + 1) = 9 × 2 = 18
Example 2: Find the Least Common Multiple and Highest Common Factor (HCF) of 1280 and 1153.

Solution:

The factors of 1280 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 256, 320, 640, 1280 and factors of 1153 are 1, 1153.

Therefore, the Least Common Multiple of 1280 and 1153 is 1475840 and Highest Common Factor (HCF) of 1280 and 1153 is 1.
Example 3: Find if 4, 5, 16, 80, 128, 256, 640 and 813 are factors of 1280.

Solution:

When we divide 1280 by 813 it leaves a remainder. Therefore, the number 813 is not a factor of 1280. All numbers except 813 are factors of 1280.
Example 4: Find the product of all the prime factors of 1280.

Solution:

Since, the prime factors of 1280 are 2, 5. Therefore, the product of prime factors = 2 × 5 = 10.

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FAQs on Factors of 1280

What are the Factors of 1280?

The factors of 1280 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 256, 320, 640, 1280 and its negative factors are -1, -2, -4, -5, -8, -10, -16, -20, -32, -40, -64, -80, -128, -160, -256, -320, -640, -1280.

What is the Sum of the Factors of 1280?

Sum of all factors of 1280 = (2^{8 + 1} - 1)/(2 - 1) × (5^{1 + 1} - 1)/(5 - 1) = 3066

What are Pair Factors of 1280?

The pair factors of 1280 are (1, 1280), (2, 640), (4, 320), (5, 256), (8, 160), (10, 128), (16, 80), (20, 64), (32, 40).

What is the Greatest Common Factor of 1280 and 131?

The factors of 1280 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 256, 320, 640, 1280 and the factors of 131 are 1, 131. 1280 and 131 have only one common factor which is 1. This implies that 1280 and 131 are co-prime.

Hence, the Greatest Common Factor (GCF) of 1280 and 131 is 1.

How Many Factors of 1280 are also Factors of 1064?

Since, the factors of 1280 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 256, 320, 640, 1280 and the factors of 1064 are 1, 2, 4, 7, 8, 14, 19, 28, 38, 56, 76, 133, 152, 266, 532, 1064.
Hence, [1, 2, 4, 8] are the common factors of 1280 and 1064.

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