A day full of math games & activities. Find one near you.

Factors of 1540

Factors of 1540 are numbers that, when multiplied in pairs give the product as 1540. There are 24 factors of 1540, of which the following are its prime factors 2, 5, 7, 11. The Prime Factorization of 1540 is 2² × 5¹ × 7¹ × 11¹.

All Factors of 1540: 1, 2, 4, 5, 7, 10, 11, 14, 20, 22, 28, 35, 44, 55, 70, 77, 110, 140, 154, 220, 308, 385, 770 and 1540
Prime Factors of 1540: 2, 5, 7, 11
Prime Factorization of 1540: 2² × 5¹ × 7¹ × 11¹
Sum of Factors of 1540: 4032

1.	What Are the Factors of 1540?
2.	Factors of 1540 by Prime Factorization
3.	Factors of 1540 in Pairs
4.	FAQs on Factors of 1540

What are Factors of 1540?

Factors of 1540 are pairs of those numbers whose products result in 1540. These factors are either prime numbers or composite numbers.

How to Find the Factors of 1540?

To find the factors of 1540, we will have to find the list of numbers that would divide 1540 without leaving any remainder.

1540/110 = 14; therefore, 110 is a factor of 1540 and 14 is also a factor of 1540.
1540/22 = 70; therefore, 22 is a factor of 1540 and 70 is also a factor of 1540.

Similarly we can find other factors. Hence, the factors of 1540 are 1, 2, 4, 5, 7, 10, 11, 14, 20, 22, 28, 35, 44, 55, 70, 77, 110, 140, 154, 220, 308, 385, 770, 1540.

☛ Also Check:

Factors of 42 - The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
Factors of 10 - The factors of 10 are 1, 2, 5, 10
Factors of 13 - The factors of 13 are 1, 13
Factors of 24 - The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24
Factors of 52 - The factors of 52 are 1, 2, 4, 13, 26, 52

Factors of 1540 by Prime Factorization

The number 1540 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 1540. The first step is to divide the number 1540 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.

1540 ÷ 2 = 770
770 ÷ 2 = 385

Further dividing 385 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 385 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 1540 can be written as 2² × 5¹ × 7¹ × 11¹ where 2, 5, 7, 11 are prime.

Factors of 1540 in Pairs

Pair factors of 1540 are the pairs of numbers that when multiplied give the product 1540. The factors of 1540 in pairs are:

1 × 1540 = (1, 1540)
2 × 770 = (2, 770)
4 × 385 = (4, 385)
5 × 308 = (5, 308)
7 × 220 = (7, 220)
10 × 154 = (10, 154)
11 × 140 = (11, 140)
14 × 110 = (14, 110)
20 × 77 = (20, 77)
22 × 70 = (22, 70)
28 × 55 = (28, 55)
35 × 44 = (35, 44)

Negative pair factors of 1540 are:

-1 × -1540 = (-1, -1540)
-2 × -770 = (-2, -770)
-4 × -385 = (-4, -385)
-5 × -308 = (-5, -308)
-7 × -220 = (-7, -220)
-10 × -154 = (-10, -154)
-11 × -140 = (-11, -140)
-14 × -110 = (-14, -110)
-20 × -77 = (-20, -77)
-22 × -70 = (-22, -70)
-28 × -55 = (-28, -55)
-35 × -44 = (-35, -44)

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

Factors of 1540 Solved Examples

Example 1: How many factors are there for 1540?

Solution:

The factors of 1540 are too many, therefore if we can find the prime factorization of 1540, 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 1540 = 2² × 5¹ × 7¹ × 11¹
Therefore, the total number of factors are (2 + 1) × (1 + 1) × (1 + 1) × (1 + 1) = 3 × 2 × 2 × 2 = 24
Example 2: Find the Least Common Multiple (LCM) and Greatest Common Divisor (GCD) of 1540 and 129.

Solution:

The factors of 1540 are 1, 2, 4, 5, 7, 10, 11, 14, 20, 22, 28, 35, 44, 55, 70, 77, 110, 140, 154, 220, 308, 385, 770, 1540 and factors of 129 are 1, 3, 43, 129.

Therefore, the Least Common Multiple (LCM) of 1540 and 129 is 198660 and Greatest Common Divisor (GCD) of 1540 and 129 is 1.
Example 3: Find if 1, 5, 11, 22, 44, 220, 1266 and 1540 are factors of 1540.

Solution:

When we divide 1540 by 1266 it leaves a remainder. Therefore, the number 1266 is not a factor of 1540. All numbers except 1266 are factors of 1540.
Example 4: Find the product of all the prime factors of 1540.

Solution:

Since, the prime factors of 1540 are 2, 5, 7, 11. Therefore, the product of prime factors = 2 × 5 × 7 × 11 = 770.

go to slide go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

go to slide go to slide go to slide go to slide go to slide

FAQs on Factors of 1540

What are the Factors of 1540?

The factors of 1540 are 1, 2, 4, 5, 7, 10, 11, 14, 20, 22, 28, 35, 44, 55, 70, 77, 110, 140, 154, 220, 308, 385, 770, 1540 and its negative factors are -1, -2, -4, -5, -7, -10, -11, -14, -20, -22, -28, -35, -44, -55, -70, -77, -110, -140, -154, -220, -308, -385, -770, -1540.

What is the Sum of all the Factors of 1540?

Sum of all factors of 1540 = (2^{2 + 1} - 1)/(2 - 1) × (5^{1 + 1} - 1)/(5 - 1) × (7^{1 + 1} - 1)/(7 - 1) × (11^{1 + 1} - 1)/(11 - 1) = 4032

What Numbers are the Prime Factors of 1540?

The prime factors of 1540 are 2, 5, 7, 11.

What is the Greatest Common Factor of 1540 and 655?

The factors of 1540 and 655 are 1, 2, 4, 5, 7, 10, 11, 14, 20, 22, 28, 35, 44, 55, 70, 77, 110, 140, 154, 220, 308, 385, 770, 1540 and 1, 5, 131, 655 respectively.

Common factors of 1540 and 655 are [1, 5].

Hence, the Greatest Common Factor of 1540 and 655 is 5.

How Many Factors of 1246 are also common to the Factors of 1540?

Since, the factors of 1540 are 1, 2, 4, 5, 7, 10, 11, 14, 20, 22, 28, 35, 44, 55, 70, 77, 110, 140, 154, 220, 308, 385, 770, 1540 and the factors of 1246 are 1, 2, 7, 14, 89, 178, 623, 1246.
Hence, [1, 2, 7, 14] are the common factors of 1540 and 1246.

Math worksheets and
visual curriculum