The greatest common divisor (GCD) of 60 and 160 is 20.
To find the GCD, we can use the method of listing the factors of each number:
- Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
- Factors of 160: 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160
Next, we identify the common factors: 1, 2, 4, 5, 10, and 20. Among these, the greatest is 20. Therefore, the GCD of 60 and 160 is 20.
Another method to find the GCD is the prime factorization method. The prime factorization of 60 is 2 × 2 × 3 × 5 or 2² × 3 × 5, and for 160, it is 2 × 2 × 2 × 2 × 5 or 2⁴ × 5. The GCD is found by taking the lowest power of each common prime factor, which gives us 2² (from 60) and 5¹ (common to both), resulting in 2² × 5 = 4 × 5 = 20.