Factors of 767
Factors of 767 are numbers that, when multiplied in pairs give the product as 767. There are overall 4 factors of 767 among which 767 is the biggest factor and 1, 13, 59, 767 are positive factors. The sum of all factors of 767 is 840. Its Prime Factors are 13 × 59 and (1, 767), (13, 59) are Pair Factors.
- All Factors of 767: 1, 13, 59 and 767
- Negative Factors of 767: -1, -13, -59 and -767
- Prime Factors of 767: 13, 59
- Prime Factorization of 767: 131 × 591
- Sum of Factors of 767: 840
1. | What Are the Factors of 767? |
2. | Factors of 767 by Prime Factorization |
3. | Factors of 767 in Pairs |
4. | FAQs on Factors of 767 |
What are Factors of 767?
Factors of 767 are pairs of those numbers whose products result in 767. These factors are either prime numbers or composite numbers.
How to Find the Factors of 767?
To find the factors of 767, we will have to find the list of numbers that would divide 767 without leaving any remainder.
- 767/59 = 13; therefore, 59 is a factor of 767 and 13 is also a factor of 767.
- 767/767 = 1; therefore, 767 is a factor of 767 and 1 is also a factor of 767.
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- Factors of 10 - The factors of 10 are 1, 2, 5, 10
Factors of 767 by Prime Factorization
- 767 ÷ 13 = 59
Further dividing 59 by 13 gives a non-zero remainder. So we stop the process and continue dividing the number 59 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 767 can be written as 131 × 591 where 13, 59 are prime.
Factors of 767 in Pairs
Pair factors of 767 are the pairs of numbers that when multiplied give the product 767. The factors of 767 in pairs are:
- 1 × 767 = (1, 767)
- 13 × 59 = (13, 59)
Negative pair factors of 767 are:
- -1 × -767 = (-1, -767)
- -13 × -59 = (-13, -59)
NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.
Factors of 767 Solved Examples
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Example 1: How many factors are there for 767?
Solution:
The factors of 767 are 1, 13, 59, 767. Therefore, 767 has 4 factors.
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Example 2: Find the Least Common Multiple and Greatest Common Divisor (GCD) of 767 and 442.
Solution:
The factors of 767 are 1, 13, 59, 767 and factors of 442 are 1, 2, 13, 17, 26, 34, 221, 442.
Therefore, the Least Common Multiple of 767 and 442 is 26078 and Greatest Common Divisor (GCD) of 767 and 442 is 13. -
Example 3: Find if 13, 162 and 767 are factors of 767.
Solution:
When we divide 767 by 162 it leaves a remainder. Therefore, the number 162 is not a factor of 767. All numbers except 162 are factors of 767.
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Example 4: Find the product of all the prime factors of 767.
Solution:
Since, the prime factors of 767 are 13, 59. Therefore, the product of prime factors = 13 × 59 = 767.
FAQs on Factors of 767
What are the Factors of 767?
The factors of 767 are 1, 13, 59, 767 and its negative factors are -1, -13, -59, -767.
What is the Sum of Factors of 767?
Factors of 767 are 1, 13, 59, 767 and, the sum of all these factors is 1 + 13 + 59 + 767 = 840
What are Pair Factors of 767?
The pair factors of 767 are (1, 767), (13, 59).
What is the Greatest Common Factor of 767 and 628?
The factors of 767 are 1, 13, 59, 767 and the factors of 628 are 1, 2, 4, 157, 314, 628. 767 and 628 have only one common factor which is 1. This implies that 767 and 628 are co-prime.
Hence, the Greatest Common Factor (GCF) of 767 and 628 is 1.
How Many Factors of 767 are also common to the Factors of 585?
Since, the factors of 767 are 1, 13, 59, 767 and the factors of 585 are 1, 3, 5, 9, 13, 15, 39, 45, 65, 117, 195, 585.
Hence, [1, 13] are the common factors of 767 and 585.
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