Find the greatest common factor of 31 and 93
The greatest common factor of 31 and 93 is 31.
thats correct
To find the greatest common factor (GCF) of two numbers, we need to determine the largest number that evenly divides both numbers.
Let's start by listing the factors of each number:
Factors of 31: 1, 31
Factors of 93: 1, 3, 31, 93
The only common factor between 31 and 93 is 1. Since 1 is the largest number that evenly divides both numbers, it is the GCF of 31 and 93.
To find the greatest common factor (GCF) of two numbers, you can use a method called prime factorization. Here's how to do it:
Step 1: Write down the prime factorization of each number.
To find the prime factorization of a number, you need to determine the prime numbers that can divide into that number, repeatedly dividing until you reach a point where the quotient is a prime number.
Prime factorization of 31:
31 is already a prime number, so the prime factorization of 31 is just 31.
Prime factorization of 93:
You can start by dividing 93 by the smallest prime number, 2. However, 93 is not divisible by 2. Next, you can try dividing by 3:
93 ÷ 3 = 31
Now you have obtained the prime factorization of 93, which is 3 x 31.
Step 2: Identify the common prime factors.
To find the GCF, you need to identify the prime numbers that are common to the factorizations of both numbers. In this case, the only common prime factor is 31.
Step 3: Multiply the common prime factors.
To find the GCF, you need to multiply all the common prime factors together. In this case, the GCF of 31 and 93 is simply 31.
Therefore, the greatest common factor of 31 and 93 is 31.