Vince has three pieces of rope with lengths of 300cm, 321cm, and 396cm. He wants to cut the three pieces of rope into smaller pieces of equal length with none left over what is the greatest possible length of each of the smaller pieces of rope?
To find the greatest possible length of each of the smaller pieces of rope, we need to find the greatest common factor (GCF) of 300, 321, and 396. The GCF is the largest number that divides evenly into all three numbers.
To find the GCF, we can factor each number into its prime factorization. The prime factorization of 300 is 2 * 2 * 3 * 5 * 5, the prime factorization of 321 is 3 * 107, and the prime factorization of 396 is 2 * 2 * 3 * 3 * 11.
The common factors of 300, 321, and 396 are 3 and 2. The GCF is the product of the common factors, which is 6.
Therefore, the greatest possible length of each of the smaller pieces of rope is 6 cm.
