# Can Pythagorean triples have common factors?

## Can Pythagorean triples have common factors?

Pythagorean triples are relatively prime. Relatively prime means they have no common divisor other than 1, even if the numbers are not prime numbers, like 14 and 15. The number 14 has factors 1, 2, 7, and 14; the number 15 has factors 1, 3, 5, and 15. Their only common factor is 1.

What are the 5 primitive Pythagorean triples?

Of these, only 16 are primitive triplets with hypotenuse less than 100: (3, 4,5), (5, 12, 13), (8, 15, 17), (7, 24, 25), (20, 21, 29), (12, 35, 37), (9, 40, 41), (28, 45, 53), (11, 60, 61), (33, 56, 65), (16, 63, 65), (48, 55, 73), (36, 77, 85), (13, 84, 85), (39, 80, 89), and (65, 72, 97) (OEIS A046086, A046087, and …

### What are the 4 most common Pythagorean triples?

Identify Common Pythagorean Triples

Triple Triple x 2 Triple x 4
3-4-5 6-8-10 12-16-20
5-12-13 10-24-26 20-48-52
7-24-25 14-48-50 28-96-100
9-40-41 18-80-82 36-160-164

Are 8 15 and 17 a Pythagorean triple?

A triplet (a, b, c) is called Pythagorean if the sum of the squares of the two smallest numbers is equal to the square of the biggest number. Hence, (8, 15, 17) is a Pythagorean triplet. Hence, (18, 80, 82) is a Pythagorean triplet.

## What are examples of Pythagorean triples?

Other examples of commonly used Pythagorean triples include: (3, 4, 5), (5, 12, 13), (8, 15, 17), (7, 24, 25) , (20, 21, 29) , (12, 35, 37), (9, 40, 41), (28, 45, 53), (11, 60, 61), (16, 63, 65), (33, 56, 65), (48, 55, 73), etc.

Does 4 5 6 represent a Pythagorean triple?

For a set of three numbers to be pythagorean, the square of the largest number should be equal to sum of the squares of other two. Hence 4 , 5 and 6 are not pythagorean triple.

### Does each set of numbers form a Pythagorean Triple explain 4 5 6?

Explanation: For a set of three numbers to be pythagorean, the square of the largest number should be equal to sum of the squares of other two. Hence 4 , 5 and 6 are not pythagorean triple.

Can a 30 40 50 Make a right triangle?

Pythagoras’s Theorem states that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the lengths of the other two sides. Actually a 30 , 40 , 50 triangle is just a scaled up 3 , 4 , 5 triangle, which is a well known right angled triangle.