Common Factors of 17 and 51

The common factor of 17 and 51 is 1. There are different methods to find the common factors of two or more numbers. Let’s focus on the listing factors method.

Let’s use the listing factors method here. The first step is to list all the factors of 17 and 51 separately. Once the factors of both numbers are listed, we can compare them and identify the common factors.

Step 1: List all the factors

Factors of 17: 1, 17

Factors of 51: 1, 3, 17, 51

Step 2: Compare and identify common factors 1 is the number that appears in both lists of factors.

Therefore, it is the only common factor of 17 and 51.

As mentioned earlier, there are different methods to find the common factors. We’ve already seen the listing factors method, and this section discusses the other commonly used methods.

Prime Factorization: For large numbers, finding the common factors using the listing factors method is quite laborious. Hence, we use the prime factorization method, where we find the prime factorization of each number to identify the common prime factors. Since 17 is prime, it only has itself and 1 as factors. The prime factors of 51 are 3 and 17. Therefore, 1 is the only common factor.

Venn Diagram: Students who are good at visualization are encouraged to use this method, as it combines prime factorization and visual thinking. The first step is to prime factor each number and place the factors in a Venn diagram. The overlapping section shows the shared primes; multiply them to get the GCF. Here, the only common factor is 1.

Division Ladder Method: The first step is to find all the prime numbers that can divide the given numbers without leaving any remainder. Once we have all the prime numbers, multiply them to get the GCF. Since the numbers in this case are relatively small, the common factor is simply 1.

• Factor – When a number divides another number without leaving a remainder, it is known as a factor of that number.

• Greatest Common Factor (GCF) – The biggest number that exactly divides all given numbers.

• Prime Number – A number that has exactly two distinct positive divisors: 1 and itself.

• Prime Factorization – The method of breaking down a number into the product of prime numbers.

• Listing Factors Method – The method of listing out all factors of all given numbers and comparing them to find the common factors.