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Factors of 680

Factors of 680 are the list of integers that can be evenly divided into 680. There are overall 16 factors of 680 among which 680 is the biggest factor and its prime factors are 2, 5, 17. The Prime Factorization of 680 is 2³ × 5¹ × 17¹.

All Factors of 680: 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340 and 680
Prime Factors of 680: 2, 5, 17
Prime Factorization of 680: 2³ × 5¹ × 17¹
Sum of Factors of 680: 1620

1.	What Are the Factors of 680?
2.	Factors of 680 by Prime Factorization
3.	Factors of 680 in Pairs
4.	FAQs on Factors of 680

What are Factors of 680?

Factors of 680 are pairs of those numbers whose products result in 680. These factors are either prime numbers or composite numbers.

How to Find the Factors of 680?

To find the factors of 680, we will have to find the list of numbers that would divide 680 without leaving any remainder.

680/5 = 136; therefore, 5 is a factor of 680 and 136 is also a factor of 680.
680/340 = 2; therefore, 340 is a factor of 680 and 2 is also a factor of 680.

Similarly we can find other factors. Hence, the factors of 680 are 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680.

☛ Also Check:

Factors of 11 - The factors of 11 are 1, 11
Factors of 48 - The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Factors of 9 - The factors of 9 are 1, 3, 9
Factors of 34 - The factors of 34 are 1, 2, 17, 34
Factors of 56 - The factors of 56 are 1, 2, 4, 7, 8, 14, 28, 56

Factors of 680 by Prime Factorization

The number 680 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 680. The first step is to divide the number 680 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.

680 ÷ 2 = 340
340 ÷ 2 = 170
170 ÷ 2 = 85

Further dividing 85 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 85 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 680 can be written as 2³ × 5¹ × 17¹ where 2, 5, 17 are prime.

Factors of 680 in Pairs

Pair factors of 680 are the pairs of numbers that when multiplied give the product 680. The factors of 680 in pairs are:

1 × 680 = (1, 680)
2 × 340 = (2, 340)
4 × 170 = (4, 170)
5 × 136 = (5, 136)
8 × 85 = (8, 85)
10 × 68 = (10, 68)
17 × 40 = (17, 40)
20 × 34 = (20, 34)

Negative pair factors of 680 are:

-1 × -680 = (-1, -680)
-2 × -340 = (-2, -340)
-4 × -170 = (-4, -170)
-5 × -136 = (-5, -136)
-8 × -85 = (-8, -85)
-10 × -68 = (-10, -68)
-17 × -40 = (-17, -40)
-20 × -34 = (-20, -34)

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

Factors of 680 Solved Examples

Example 1: How many factors are there for 680?

Solution:

The factors of 680 are too many, therefore if we can find the prime factorization of 680, 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 680 = 2³ × 5¹ × 17¹
Therefore, the total number of factors are (3 + 1) × (1 + 1) × (1 + 1) = 4 × 2 × 2 = 16
Example 2: Find the Least Common Multiple (LCM) and Highest Common Factor (HCF) of 680 and 383.

Solution:

The factors of 680 are 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680 and factors of 383 are 1, 383.

Therefore, the Least Common Multiple (LCM) of 680 and 383 is 260440 and Highest Common Factor (HCF) of 680 and 383 is 1.
Example 3: Find if 1, 2, 5, 10, 34, 85, 340 and 509 are factors of 680.

Solution:

When we divide 680 by 509 it leaves a remainder. Therefore, the number 509 is not a factor of 680. All numbers except 509 are factors of 680.
Example 4: Find the product of all the prime factors of 680.

Solution:

Since, the prime factors of 680 are 2, 5, 17. Therefore, the product of prime factors = 2 × 5 × 17 = 170.

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FAQs on Factors of 680

What are the Factors of 680?

The factors of 680 are 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680 and its negative factors are -1, -2, -4, -5, -8, -10, -17, -20, -34, -40, -68, -85, -136, -170, -340, -680.

What is the Sum of all Factors of 680?

Sum of all factors of 680 = (2^{3 + 1} - 1)/(2 - 1) × (5^{1 + 1} - 1)/(5 - 1) × (17^{1 + 1} - 1)/(17 - 1) = 1620

What are the Prime Factors of 680?

The prime factors of 680 are 2, 5, 17.

What is the Greatest Common Factor of 680 and 338?

The factors of 680 and 338 are 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680 and 1, 2, 13, 26, 169, 338 respectively.

Common factors of 680 and 338 are [1, 2].

Hence, the Greatest Common Factor of 680 and 338 is 2.

How Many Factors of 560 are also common to the Factors of 680?

Since, the factors of 680 are 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680 and the factors of 560 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, 560.
Hence, [1, 2, 4, 5, 8, 10, 20, 40] are the common factors of 680 and 560.

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