Factors of 686
Factors of 686 are the list of integers that we can split evenly into 686. There are overall 8 factors of 686 i.e. 1, 2, 7, 14, 49, 98, 343, 686 where 686 is the biggest factor. The sum of all factors of 686 is 1200 and its factors in Pairs are (1, 686), (2, 343), (7, 98), (14, 49).
- All Factors of 686: 1, 2, 7, 14, 49, 98, 343 and 686
- Negative Factors of 686: -1, -2, -7, -14, -49, -98, -343 and -686
- Prime Factors of 686: 2, 7
- Prime Factorization of 686: 21 × 73
- Sum of Factors of 686: 1200
1. | What Are the Factors of 686? |
2. | Factors of 686 by Prime Factorization |
3. | Factors of 686 in Pairs |
4. | FAQs on Factors of 686 |
What are Factors of 686?
Factors of 686 are pairs of those numbers whose products result in 686. These factors are either prime numbers or composite numbers.
How to Find the Factors of 686?
To find the factors of 686, we will have to find the list of numbers that would divide 686 without leaving any remainder.
- 686/98 = 7; therefore, 98 is a factor of 686 and 7 is also a factor of 686.
- 686/14 = 49; therefore, 14 is a factor of 686 and 49 is also a factor of 686.
☛ Also Check:
- Factors of 37 - The factors of 37 are 1, 37
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- Factors of 11 - The factors of 11 are 1, 11
- Factors of 50 - The factors of 50 are 1, 2, 5, 10, 25, 50
- Factors of 33 - The factors of 33 are 1, 3, 11, 33
Factors of 686 by Prime Factorization
- 686 ÷ 2 = 343
Further dividing 343 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 343 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 686 can be written as 21 × 73 where 2, 7 are prime.
Factors of 686 in Pairs
Pair factors of 686 are the pairs of numbers that when multiplied give the product 686. The factors of 686 in pairs are:
- 1 × 686 = (1, 686)
- 2 × 343 = (2, 343)
- 7 × 98 = (7, 98)
- 14 × 49 = (14, 49)
Negative pair factors of 686 are:
- -1 × -686 = (-1, -686)
- -2 × -343 = (-2, -343)
- -7 × -98 = (-7, -98)
- -14 × -49 = (-14, -49)
NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.
Factors of 686 Solved Examples
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Example 1: How many factors are there for 686?
Solution:
The factors of 686 are 1, 2, 7, 14, 49, 98, 343, 686. Therefore, 686 has 8 factors.
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Example 2: Find the Lowest Common Multiple (LCM) and Greatest Common Factor (GCF) of 686 and 680.
Solution:
The factors of 686 are 1, 2, 7, 14, 49, 98, 343, 686 and factors of 680 are 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680.
Therefore, the Lowest Common Multiple (LCM) of 686 and 680 is 233240 and Greatest Common Factor (GCF) of 686 and 680 is 2. -
Example 3: Find if 1, 7, 49, 98 and 302 are factors of 686.
Solution:
When we divide 686 by 302 it leaves a remainder. Therefore, the number 302 is not a factor of 686. All numbers except 302 are factors of 686.
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Example 4: Find the product of all the prime factors of 686.
Solution:
Since, the prime factors of 686 are 2, 7. Therefore, the product of prime factors = 2 × 7 = 14.
FAQs on Factors of 686
What are the Factors of 686?
The factors of 686 are 1, 2, 7, 14, 49, 98, 343, 686 and its negative factors are -1, -2, -7, -14, -49, -98, -343, -686.
What is the Sum of the Factors of 686?
Sum of all factors of 686 = (21 + 1 - 1)/(2 - 1) × (73 + 1 - 1)/(7 - 1) = 1200
What are the Prime Factors of 686?
The prime factors of 686 are 2, 7.
What is the Greatest Common Factor of 686 and 447?
The factors of 686 are 1, 2, 7, 14, 49, 98, 343, 686 and the factors of 447 are 1, 3, 149, 447. 686 and 447 have only one common factor which is 1. This implies that 686 and 447 are co-prime.
Hence, the Greatest Common Factor (GCF) of 686 and 447 is 1.
How Many Factors of 686 are also Factors of 100?
Since, the factors of 686 are 1, 2, 7, 14, 49, 98, 343, 686 and the factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100.
Hence, [1, 2] are the common factors of 686 and 100.
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