Find the length of shhortest piece of string that can b cut in to equal length of 16cm, 20cm,24cm
To find the length of the shortest piece of string that can be cut into equal lengths of 16cm, 20cm, and 24cm, we need to find the greatest common divisor (GCD) of the three given numbers.
Step 1: List the prime factors of each number:
- 16 = 2^4
- 20 = 2^2 * 5
- 24 = 2^3 * 3
Step 2: Determine the common factors:
Since we are looking for the GCD, we need to find the highest power of each prime factor that is common to all three numbers.
From the prime factorization, we see that 2 is a common factor with the highest power of 2 in the exponents of 4, 2, and 3. Therefore, 2^2 = 4 is the common factor of 16, 20, and 24.
Step 3: Calculate the GCD:
The GCD of the three numbers is the product of the common factors. In this case, the GCD is 2^2 * 1 (since there are no other common factors besides 2^2).
Step 4: Find the length of the shortest piece of string:
To find the length of the shortest piece of string, we multiply the GCD by the number of pieces we want, which is 3 in this case.
Length of the shortest piece of string = GCD * number of pieces
Length of the shortest piece of string = 4 * 3
Length of the shortest piece of string = 12 cm
Therefore, the length of the shortest piece of string that can be cut into equal lengths of 16cm, 20cm, and 24cm is 12cm.