Benita has 3 ropes measuring 54 centimeters, 108 centimeters and 189 centimeters. She cuts all of them into equal pieces. The length of each piece is the longest possible length she can cut. What is the length of each piece of cut rope? How many pieces of rope does Benita get?
Find the Highest common factor of the 3 numbers.
Each of the numbers will be divisible by that number to get the number of pieces.
12 meter annd 14 meter
54 cm's & 6 nos
13 pieces
27 centumeters
Benita has three ropes measuring 54 centimeters, 108 centimeters, and 189 centimeters. She cuts all of them into equal pieces. The length of each piece is the longest possible length she can cut.
What is the length of each piece of cut rope?
3|54,108,189
3|18,36,63
3|6,12,21
2,4,7
GCF = 27
Answer: 27cm
How many pieces of cut rope does Benita get?
Answer: 2+4+7 = 13 pieces of cut rope
Check:
54/27 = 2
108/27 = 4
189/27 = 7
To find the length of each piece of cut rope, we need to determine the greatest common divisor (GCD) of the rope lengths. The GCD is the largest length that evenly divides all the given lengths.
Step 1: Find the GCD of the rope lengths (54, 108, and 189).
- The prime factorization of 54: 2 * 3^3
- The prime factorization of 108: 2^2 * 3^3
- The prime factorization of 189: 3^3 * 7
Step 2: Identify the common prime factors and their lowest exponent.
- The common prime factors are 2 and 3.
- The lowest exponent for 2 is 2.
- The lowest exponent for 3 is 3.
Step 3: Calculate the GCD by multiplying the common factors with the lowest exponents.
- GCD = 2^2 * 3^3 = 4 * 27 = 108 centimeters
So, the length of each piece of cut rope is 108 centimeters.
To find the number of pieces of rope Benita gets, we need to divide the original rope length by the length of each piece.
For the first rope: 54 cm ÷ 108 cm = 0.5 piece
For the second rope: 108 cm ÷ 108 cm = 1 piece
For the third rope: 189 cm ÷ 108 cm ≈ 1.75 pieces
Since we're looking for the whole number of pieces, Benita will get 0.5 + 1 + 1.75 = 3.25 pieces of rope. However, since we cannot have fractional pieces of rope, we round down to the nearest whole number.
Therefore, Benita gets a total of 3 pieces of rope.