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# Why can two prime numbers only have one common factor?

Updated: 4/28/2022

Wiki User

10y ago

Each Prime number only has two factors: one and itself. The only factor any set of prime numbers has in common is 1.

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10y ago

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Q: Why can two prime numbers only have one common factor?
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### What is the greatest common factor of 2 or more prime numbers?

As the numbers are all prime, the only factors each of them has are 1 and the number itself. Therefore the greatest, and only, common factor of two of more prime numbers is 1.

### What is the greatest common factor of 5 and 23?

Because both numbers are prime numbers, the only common factor they have is 1. Therefore, the greatest common factor is 1. Another way to determine the greatest common factor is to find all the factors of the numbers and compare them. The factors of 5 are 1 and 5. The factors of 23 are 1 and 23. The only common factor is 1. Therefore, the greatest common factor is 1, which means the numbers are relatively prime. The greatest common factor can also be calculated by identifying the common prime factors and multiplying them together. The prime factor of 5 is 5. The prime factor of 23 is 23. There are no prime factors in common, so the numbers are relatively prime, which means the greatest common factor is 1.

### What is the greatest common factor of two prime numbers?

The greatest common factor of two different prime numbers is 1. The two prime numbers have as their factors, 1 and themselves. That means that 1 is the only factor they have in common.The GCF is 1.

### Are 40 and 395 relatively prime?

No because their only common factor is not 1. Relatively prime numbers only have 1 as a common factor. They both have 1 but also 5 as a common factor.

### What are the common factor of of 334 and 567?

The numbers are co-prime so the only common factor is 1.

### What are two relatively prime numbers?

Numbers whose only common factor is 1.

### What do the numbers 12 49 and 45 have in common?

Their only common factor is 1. They each have a repeated prime factor.

### When a pair of numbers have ONLY 1 as the common factor what is it called?

relatively prime or co-prime.

### Two numbers having only 1 as common factor is called?

They are called prime numbers.

### What the smallest common factor between 19 and 31?

The least common factor of any set of numbers is 1.

### Two prime numbers greater than 2 have 2 as a common factor?

No prime number greater than 2 has 2 as a factor. A prime number has only two factors, 1 and the number itself. All prime numbers have 1 as a common factor. Numbers with any number besides 1 as common factors are composite numbers.

### What makes two or more numbers relatively prime?

Two numbers are relatively prime if the only factor they have in common is 1. Example: 12 and 17 are relatively prime because they have only 1 as a common factor. 12 and 21 are not relatively prime because they have 1 and 3 as common factors.