Factors of 760

Factors of 760 are the list of integers that we can split evenly into 760. There are overall 16 factors of 760, of which 2, 5, 19 are its prime factors. The sum of all factors of 760 is 1800.

All Factors of 760: 1, 2, 4, 5, 8, 10, 19, 20, 38, 40, 76, 95, 152, 190, 380 and 760
Prime Factors of 760: 2, 5, 19
Prime Factorization of 760: 2³ × 5¹ × 19¹
Sum of Factors of 760: 1800

1.	What Are the Factors of 760?
2.	Factors of 760 by Prime Factorization
3.	Factors of 760 in Pairs
4.	FAQs on Factors of 760

What are Factors of 760?

Factors of 760 are pairs of those numbers whose products result in 760. These factors are either prime numbers or composite numbers.

How to Find the Factors of 760?

To find the factors of 760, we will have to find the list of numbers that would divide 760 without leaving any remainder.

760/5 = 152; therefore, 5 is a factor of 760 and 152 is also a factor of 760.
760/95 = 8; therefore, 95 is a factor of 760 and 8 is also a factor of 760.

Similarly we can find other factors. Hence, the factors of 760 are 1, 2, 4, 5, 8, 10, 19, 20, 38, 40, 76, 95, 152, 190, 380, 760.

☛ Also Check:

Factors of 56 - The factors of 56 are 1, 2, 4, 7, 8, 14, 28, 56
Factors of 31 - The factors of 31 are 1, 31
Factors of 81 - The factors of 81 are 1, 3, 9, 27, 81
Factors of 29 - The factors of 29 are 1, 29
Factors of 30 - The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30

Factors of 760 by Prime Factorization

The number 760 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 760. The first step is to divide the number 760 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.

760 ÷ 2 = 380
380 ÷ 2 = 190
190 ÷ 2 = 95

Further dividing 95 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 95 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 760 can be written as 2³ × 5¹ × 19¹ where 2, 5, 19 are prime.

Factors of 760 in Pairs

Pair factors of 760 are the pairs of numbers that when multiplied give the product 760. The factors of 760 in pairs are:

1 × 760 = (1, 760)
2 × 380 = (2, 380)
4 × 190 = (4, 190)
5 × 152 = (5, 152)
8 × 95 = (8, 95)
10 × 76 = (10, 76)
19 × 40 = (19, 40)
20 × 38 = (20, 38)

Negative pair factors of 760 are:

-1 × -760 = (-1, -760)
-2 × -380 = (-2, -380)
-4 × -190 = (-4, -190)
-5 × -152 = (-5, -152)
-8 × -95 = (-8, -95)
-10 × -76 = (-10, -76)
-19 × -40 = (-19, -40)
-20 × -38 = (-20, -38)

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

Factors of 760 Solved Examples

Example 1: How many factors are there for 760?

Solution:

The factors of 760 are too many, therefore if we can find the prime factorization of 760, 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 760 = 2³ × 5¹ × 19¹
Therefore, the total number of factors are (3 + 1) × (1 + 1) × (1 + 1) = 4 × 2 × 2 = 16
Example 2: Find the Lowest Common Multiple (LCM) and Greatest Common Factor (GCF) of 760 and 669.

Solution:

The factors of 760 are 1, 2, 4, 5, 8, 10, 19, 20, 38, 40, 76, 95, 152, 190, 380, 760 and factors of 669 are 1, 3, 223, 669.

Therefore, the Lowest Common Multiple (LCM) of 760 and 669 is 508440 and Greatest Common Factor (GCF) of 760 and 669 is 1.
Example 3: Find if 8, 10, 19, 76, 190, 323, 380 and 760 are factors of 760.

Solution:

When we divide 760 by 323 it leaves a remainder. Therefore, the number 323 is not a factor of 760. All numbers except 323 are factors of 760.
Example 4: Find the product of all the prime factors of 760.

Solution:

Since, the prime factors of 760 are 2, 5, 19. Therefore, the product of prime factors = 2 × 5 × 19 = 190.

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FAQs on Factors of 760

What are the Factors of 760?

The factors of 760 are 1, 2, 4, 5, 8, 10, 19, 20, 38, 40, 76, 95, 152, 190, 380, 760 and its negative factors are -1, -2, -4, -5, -8, -10, -19, -20, -38, -40, -76, -95, -152, -190, -380, -760.

What is the Sum of the Factors of 760?

Sum of all factors of 760 = (2^{3 + 1} - 1)/(2 - 1) × (5^{1 + 1} - 1)/(5 - 1) × (19^{1 + 1} - 1)/(19 - 1) = 1800

What are Prime Factors of 760?

The prime factors of 760 are 2, 5, 19.

What is the Greatest Common Factor of 760 and 273?

The factors of 760 are 1, 2, 4, 5, 8, 10, 19, 20, 38, 40, 76, 95, 152, 190, 380, 760 and the factors of 273 are 1, 3, 7, 13, 21, 39, 91, 273. 760 and 273 have only one common factor which is 1. This implies that 760 and 273 are co-prime.

Hence, the Greatest Common Factor (GCF) of 760 and 273 is 1.

How Many Factors of 760 are also Factors of 340?

Since, the factors of 760 are 1, 2, 4, 5, 8, 10, 19, 20, 38, 40, 76, 95, 152, 190, 380, 760 and the factors of 340 are 1, 2, 4, 5, 10, 17, 20, 34, 68, 85, 170, 340.
Hence, [1, 2, 4, 5, 10, 20] are the common factors of 760 and 340.

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