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Factors of 1560

Factors of 1560 are the list of integers that can be evenly divided into 1560. There are 32 factors of 1560 of which 1560 itself is the biggest factor and its prime factors are 2, 3, 5, 13 The Prime Factorization of 1560 is 2³ × 3¹ × 5¹ × 13¹.

All Factors of 1560: 1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 20, 24, 26, 30, 39, 40, 52, 60, 65, 78, 104, 120, 130, 156, 195, 260, 312, 390, 520, 780 and 1560
Prime Factors of 1560: 2, 3, 5, 13
Prime Factorization of 1560: 2³ × 3¹ × 5¹ × 13¹
Sum of Factors of 1560: 5040

1.	What Are the Factors of 1560?
2.	Factors of 1560 by Prime Factorization
3.	Factors of 1560 in Pairs
4.	FAQs on Factors of 1560

What are Factors of 1560?

Factors of 1560 are pairs of those numbers whose products result in 1560. These factors are either prime numbers or composite numbers.

How to Find the Factors of 1560?

To find the factors of 1560, we will have to find the list of numbers that would divide 1560 without leaving any remainder.

1560/1 = 1560; therefore, 1 is a factor of 1560.
1560/390 = 4; therefore, 390 is a factor of 1560.

Similarly we can find other factors. Hence, the factors of 1560 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 20, 24, 26, 30, 39, 40, 52, 60, 65, 78, 104, 120, 130, 156, 195, 260, 312, 390, 520, 780, 1560.

☛ Also Check:

Factors of 108 - The factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
Factors of 39 - The factors of 39 are 1, 3, 13, 39
Factors of 4 - The factors of 4 are 1, 2, 4
Factors of 44 - The factors of 44 are 1, 2, 4, 11, 22, 44
Factors of 144 - The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144

Factors of 1560 by Prime Factorization

The number 1560 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 1560. The first step is to divide the number 1560 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.

1560 ÷ 2 = 780
780 ÷ 2 = 390
390 ÷ 2 = 195

Further dividing 195 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 195 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 1560 can be written as 2³ × 3¹ × 5¹ × 13¹ where 2, 3, 5, 13 are prime.

Factors of 1560 in Pairs

Pair factors of 1560 are the pairs of numbers that when multiplied give the product 1560. The factors of 1560 in pairs are:

1 × 1560 = (1, 1560)
2 × 780 = (2, 780)
3 × 520 = (3, 520)
4 × 390 = (4, 390)
5 × 312 = (5, 312)
6 × 260 = (6, 260)
8 × 195 = (8, 195)
10 × 156 = (10, 156)
12 × 130 = (12, 130)
13 × 120 = (13, 120)
15 × 104 = (15, 104)
20 × 78 = (20, 78)
24 × 65 = (24, 65)
26 × 60 = (26, 60)
30 × 52 = (30, 52)
39 × 40 = (39, 40)

Negative pair factors of 1560 are:

-1 × -1560 = (-1, -1560)
-2 × -780 = (-2, -780)
-3 × -520 = (-3, -520)
-4 × -390 = (-4, -390)
-5 × -312 = (-5, -312)
-6 × -260 = (-6, -260)
-8 × -195 = (-8, -195)
-10 × -156 = (-10, -156)
-12 × -130 = (-12, -130)
-13 × -120 = (-13, -120)
-15 × -104 = (-15, -104)
-20 × -78 = (-20, -78)
-24 × -65 = (-24, -65)
-26 × -60 = (-26, -60)
-30 × -52 = (-30, -52)
-39 × -40 = (-39, -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 1560 Solved Examples

Example 1: How many factors are there for 1560?

Solution:

The factors of 1560 are too many, therefore if we can find the prime factorization of 1560, 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 1560 = 2³ × 3¹ × 5¹ × 13¹
Therefore, the total number of factors are (3 + 1) × (1 + 1) × (1 + 1) × (1 + 1) = 4 × 2 × 2 × 2 = 32
Example 2: Find the Lowest Common Multiple (LCM) and Greatest Common Divisor (GCD) of 1560 and 1114.

Solution:

The factors of 1560 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 20, 24, 26, 30, 39, 40, 52, 60, 65, 78, 104, 120, 130, 156, 195, 260, 312, 390, 520, 780, 1560 and factors of 1114 are 1, 2, 557, 1114.

Therefore, the Lowest Common Multiple (LCM) of 1560 and 1114 is 868920 and Greatest Common Divisor (GCD) of 1560 and 1114 is 2.
Example 3: Find if 4, 5, 40, 52, 65, 390, 604 and 780 are factors of 1560.

Solution:

When we divide 1560 by 604 it leaves a remainder. Therefore, the number 604 is not a factor of 1560. All numbers except 604 are factors of 1560.
Example 4: Find the product of all the prime factors of 1560.

Solution:

Since, the prime factors of 1560 are 2, 3, 5, 13. Therefore, the product of prime factors = 2 × 3 × 5 × 13 = 390.

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FAQs on Factors of 1560

What are the Factors of 1560?

The factors of 1560 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 20, 24, 26, 30, 39, 40, 52, 60, 65, 78, 104, 120, 130, 156, 195, 260, 312, 390, 520, 780, 1560 and its negative factors are -1, -2, -3, -4, -5, -6, -8, -10, -12, -13, -15, -20, -24, -26, -30, -39, -40, -52, -60, -65, -78, -104, -120, -130, -156, -195, -260, -312, -390, -520, -780, -1560.

What is the Sum of Factors of 1560?

Sum of all factors of 1560 = (2^{3 + 1} - 1)/(2 - 1) × (3^{1 + 1} - 1)/(3 - 1) × (5^{1 + 1} - 1)/(5 - 1) × (13^{1 + 1} - 1)/(13 - 1) = 5040

What Numbers are the Prime Factors of 1560?

The prime factors of 1560 are 2, 3, 5, 13.

What is the Greatest Common Factor of 1560 and 830?

The factors of 1560 and 830 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 20, 24, 26, 30, 39, 40, 52, 60, 65, 78, 104, 120, 130, 156, 195, 260, 312, 390, 520, 780, 1560 and 1, 2, 5, 10, 83, 166, 415, 830 respectively.

Common factors of 1560 and 830 are [1, 2, 5, 10].

Hence, the GCF of 1560 and 830 is 10.

What are the Common Factors of 1560 and 1426?

Since, the factors of 1560 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 20, 24, 26, 30, 39, 40, 52, 60, 65, 78, 104, 120, 130, 156, 195, 260, 312, 390, 520, 780, 1560 and the factors of 1426 are 1, 2, 23, 31, 46, 62, 713, 1426.
Hence, [1, 2] are the common factors of 1560 and 1426.

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