Factors of 3540

Factors of 3540 are the list of integers that we can split evenly into 3540. There are total 24 factors of 3540, of which 2, 3, 5, 59 are its prime factors. The sum of all factors of 3540 is 10080.

All Factors of 3540: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 59, 60, 118, 177, 236, 295, 354, 590, 708, 885, 1180, 1770 and 3540
Prime Factors of 3540: 2, 3, 5, 59
Prime Factorization of 3540: 2² × 3¹ × 5¹ × 59¹
Sum of Factors of 3540: 10080

1.	What Are the Factors of 3540?
2.	Factors of 3540 by Prime Factorization
3.	Factors of 3540 in Pairs
4.	FAQs on Factors of 3540

What are Factors of 3540?

Factors of 3540 are pairs of those numbers whose products result in 3540. These factors are either prime numbers or composite numbers.

How to Find the Factors of 3540?

To find the factors of 3540, we will have to find the list of numbers that would divide 3540 without leaving any remainder.

3540/12 = 295; therefore, 12 is a factor of 3540 and 295 is also a factor of 3540.
3540/5 = 708; therefore, 5 is a factor of 3540 and 708 is also a factor of 3540.

Similarly we can find other factors. Hence, the factors of 3540 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 59, 60, 118, 177, 236, 295, 354, 590, 708, 885, 1180, 1770, 3540.

☛ Also Check:

Factors of 32 - The factors of 32 are 1, 2, 4, 8, 16, 32
Factors of 29 - The factors of 29 are 1, 29
Factors of 90 - The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
Factors of 40 - The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40
Factors of 70 - The factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70

Factors of 3540 by Prime Factorization

The number 3540 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 3540. The first step is to divide the number 3540 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.

3540 ÷ 2 = 1770
1770 ÷ 2 = 885

Further dividing 885 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 885 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 3540 can be written as 2² × 3¹ × 5¹ × 59¹ where 2, 3, 5, 59 are prime.

Factors of 3540 in Pairs

Pair factors of 3540 are the pairs of numbers that when multiplied give the product 3540. The factors of 3540 in pairs are:

1 × 3540 = (1, 3540)
2 × 1770 = (2, 1770)
3 × 1180 = (3, 1180)
4 × 885 = (4, 885)
5 × 708 = (5, 708)
6 × 590 = (6, 590)
10 × 354 = (10, 354)
12 × 295 = (12, 295)
15 × 236 = (15, 236)
20 × 177 = (20, 177)
30 × 118 = (30, 118)
59 × 60 = (59, 60)

Negative pair factors of 3540 are:

-1 × -3540 = (-1, -3540)
-2 × -1770 = (-2, -1770)
-3 × -1180 = (-3, -1180)
-4 × -885 = (-4, -885)
-5 × -708 = (-5, -708)
-6 × -590 = (-6, -590)
-10 × -354 = (-10, -354)
-12 × -295 = (-12, -295)
-15 × -236 = (-15, -236)
-20 × -177 = (-20, -177)
-30 × -118 = (-30, -118)
-59 × -60 = (-59, -60)

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

Factors of 3540 Solved Examples

Example 1: How many factors are there for 3540?

Solution:

The factors of 3540 are too many, therefore if we can find the prime factorization of 3540, 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 3540 = 2² × 3¹ × 5¹ × 59¹
Therefore, the total number of factors are (2 + 1) × (1 + 1) × (1 + 1) × (1 + 1) = 3 × 2 × 2 × 2 = 24
Example 2: Find the Lowest Common Multiple (LCM) and Greatest Common Divisor (GCD) of 3540 and 1527.

Solution:

The factors of 3540 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 59, 60, 118, 177, 236, 295, 354, 590, 708, 885, 1180, 1770, 3540 and factors of 1527 are 1, 3, 509, 1527.

Therefore, the Lowest Common Multiple (LCM) of 3540 and 1527 is 1801860 and Greatest Common Divisor (GCD) of 3540 and 1527 is 3.
Example 3: Find if 1, 2, 10, 12, 20, 60, 148 and 3540 are factors of 3540.

Solution:

When we divide 3540 by 148 it leaves a remainder. Therefore, the number 148 is not a factor of 3540. All numbers except 148 are factors of 3540.
Example 4: Find the product of all the prime factors of 3540.

Solution:

Since, the prime factors of 3540 are 2, 3, 5, 59. Therefore, the product of prime factors = 2 × 3 × 5 × 59 = 1770.

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FAQs on Factors of 3540

What are the Factors of 3540?

The factors of 3540 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 59, 60, 118, 177, 236, 295, 354, 590, 708, 885, 1180, 1770, 3540 and its negative factors are -1, -2, -3, -4, -5, -6, -10, -12, -15, -20, -30, -59, -60, -118, -177, -236, -295, -354, -590, -708, -885, -1180, -1770, -3540.

What is the Sum of the Factors of 3540?

Sum of all factors of 3540 = (2^{2 + 1} - 1)/(2 - 1) × (3^{1 + 1} - 1)/(3 - 1) × (5^{1 + 1} - 1)/(5 - 1) × (59^{1 + 1} - 1)/(59 - 1) = 10080

What are Prime Factors of 3540?

The prime factors of 3540 are 2, 3, 5, 59.

What is the Greatest Common Factor of 3540 and 2684?

The factors of 3540 and 2684 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 59, 60, 118, 177, 236, 295, 354, 590, 708, 885, 1180, 1770, 3540 and 1, 2, 4, 11, 22, 44, 61, 122, 244, 671, 1342, 2684 respectively.

Common factors of 3540 and 2684 are [1, 2, 4].

Hence, the Greatest Common Factor (GCF) of 3540 and 2684 is 4.

How Many Factors of 3540 are also Factors of 111?

Since, the factors of 3540 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 59, 60, 118, 177, 236, 295, 354, 590, 708, 885, 1180, 1770, 3540 and the factors of 111 are 1, 3, 37, 111.
Hence, [1, 3] are the common factors of 3540 and 111.

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