Question

what is the greatest common factor of 69 and 91?

Explanation:

Step1: Factorize 69

To find the factors of 69, we start by dividing it by prime numbers. \(69\div3 = 23\), and 23 is a prime number. So, the prime factorization of 69 is \(69 = 3\times23\). The factors of 69 are 1, 3, 23, 69.

Step2: Factorize 91

Now, factorize 91. We check divisibility by prime numbers. \(91\div7 = 13\), and both 7 and 13 are prime numbers. So, the prime factorization of 91 is \(91 = 7\times13\). The factors of 91 are 1, 7, 13, 91.

Step3: Find common factors

Now, we list the common factors of 69 and 91. From the factors of 69 (1, 3, 23, 69) and factors of 91 (1, 7, 13, 91), the only common factor is 1.

Answer:

1