Gcf of 61, 112

Answer 1

To find the greatest common factor (GCF) of 61 and 112, we can start by identifying the prime factorization of each number.

1. Prime factorization of 61:

   • 61 is a prime number, so its only factors are 1 and 61.

2. Prime factorization of 112:

   • 112 can be divided by 2:
     • \(112 ÷ 2 = 56\)
     • \(56 ÷ 2 = 28\)
     • \(28 ÷ 2 = 14\)
     • \(14 ÷ 2 = 7\)
     • So, the prime factorization of 112 is \(2^4 \times 7\).

Now, let's list the factors:

• Factors of 61: 1, 61
• Factors of 112: 1, 2, 4, 7, 8, 14, 16, 28, 56, 112

The only common factor between 61 and 112 is 1.

Thus, the GCF of 61 and 112 is 1.