Factors of 1925

Factors of 1925 are the list of integers that we can split evenly into 1925. There are total 12 factors of 1925, of which 5, 7, 11 are its prime factors. The sum of all factors of 1925 is 2976.

All Factors of 1925: 1, 5, 7, 11, 25, 35, 55, 77, 175, 275, 385 and 1925
Prime Factors of 1925: 5, 7, 11
Prime Factorization of 1925: 5² × 7¹ × 11¹
Sum of Factors of 1925: 2976

1.	What Are the Factors of 1925?
2.	Factors of 1925 by Prime Factorization
3.	Factors of 1925 in Pairs
4.	FAQs on Factors of 1925

What are Factors of 1925?

Factors of 1925 are pairs of those numbers whose products result in 1925. These factors are either prime numbers or composite numbers.

How to Find the Factors of 1925?

To find the factors of 1925, we will have to find the list of numbers that would divide 1925 without leaving any remainder.

1925/11 = 175; therefore, 11 is a factor of 1925 and 175 is also a factor of 1925.
1925/55 = 35; therefore, 55 is a factor of 1925 and 35 is also a factor of 1925.

Similarly we can find other factors. Hence, the factors of 1925 are 1, 5, 7, 11, 25, 35, 55, 77, 175, 275, 385, 1925.

☛ Also Check:

Factors of 25 - The factors of 25 are 1, 5, 25
Factors of 100 - The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100
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 26 - The factors of 26 are 1, 2, 13, 26
Factors of 34 - The factors of 34 are 1, 2, 17, 34

Factors of 1925 by Prime Factorization

The number 1925 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 1925. The first step is to divide the number 1925 with the smallest prime factor, here it is 5. We keep dividing until it gives a non-zero remainder.

1925 ÷ 5 = 385
385 ÷ 5 = 77

Further dividing 77 by 5 gives a non-zero remainder. So we stop the process and continue dividing the number 77 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 1925 can be written as 5² × 7¹ × 11¹ where 5, 7, 11 are prime.

Factors of 1925 in Pairs

Pair factors of 1925 are the pairs of numbers that when multiplied give the product 1925. The factors of 1925 in pairs are:

1 × 1925 = (1, 1925)
5 × 385 = (5, 385)
7 × 275 = (7, 275)
11 × 175 = (11, 175)
25 × 77 = (25, 77)
35 × 55 = (35, 55)

Negative pair factors of 1925 are:

-1 × -1925 = (-1, -1925)
-5 × -385 = (-5, -385)
-7 × -275 = (-7, -275)
-11 × -175 = (-11, -175)
-25 × -77 = (-25, -77)
-35 × -55 = (-35, -55)

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

Factors of 1925 Solved Examples

Example 1: How many factors are there for 1925?

Solution:

The factors of 1925 are too many, therefore if we can find the prime factorization of 1925, 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 1925 = 5² × 7¹ × 11¹
Therefore, the total number of factors are (2 + 1) × (1 + 1) × (1 + 1) = 3 × 2 × 2 = 12
Example 2: Find the Least Common Multiple and Greatest Common Divisor (GCD) of 1925 and 1207.

Solution:

The factors of 1925 are 1, 5, 7, 11, 25, 35, 55, 77, 175, 275, 385, 1925 and factors of 1207 are 1, 17, 71, 1207.

Therefore, the Least Common Multiple of 1925 and 1207 is 2323475 and Greatest Common Divisor (GCD) of 1925 and 1207 is 1.
Example 3: Find if 5, 11, 35, 55, 77, 275 and 311 are factors of 1925.

Solution:

When we divide 1925 by 311 it leaves a remainder. Therefore, the number 311 is not a factor of 1925. All numbers except 311 are factors of 1925.
Example 4: Find the product of all the prime factors of 1925.

Solution:

Since, the prime factors of 1925 are 5, 7, 11. Therefore, the product of prime factors = 5 × 7 × 11 = 385.

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FAQs on Factors of 1925

What are the Factors of 1925?

The factors of 1925 are 1, 5, 7, 11, 25, 35, 55, 77, 175, 275, 385, 1925 and its negative factors are -1, -5, -7, -11, -25, -35, -55, -77, -175, -275, -385, -1925.

What is the Sum of all Factors of 1925?

Sum of all factors of 1925 = (5^{2 + 1} - 1)/(5 - 1) × (7^{1 + 1} - 1)/(7 - 1) × (11^{1 + 1} - 1)/(11 - 1) = 2976

What are Prime Factors of 1925?

The prime factors of 1925 are 5, 7, 11.

What is the Greatest Common Factor of 1925 and 106?

The factors of 1925 are 1, 5, 7, 11, 25, 35, 55, 77, 175, 275, 385, 1925 and the factors of 106 are 1, 2, 53, 106. 1925 and 106 have only one common factor which is 1. This implies that 1925 and 106 are co-prime.

Hence, the Greatest Common Factor (GCF) of 1925 and 106 is 1.

What are the Common Factors of 1925 and 907?

Since, the factors of 1925 are 1, 5, 7, 11, 25, 35, 55, 77, 175, 275, 385, 1925 and factors of 907 are 1, 907. Hence, 1925 and 907 have only one common factor which is 1. Therefore, 1925 and 907 are co-prime.

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