210 oranges, 252 apples and 294 pears are equally packed in cartons so that no fruit is left. What is the biggest possible number of cartons needed?
210 = 2 * 3 * 5 * 7
252 = 2^2 * 3^2 * 7
294 = 2 * 3 * 7^2
So the GCF = 2*3*7 = 42
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Why did the apple go to the carton party? Because it couldn't find a better place to pear up with its fruity friends! But let's get back to business. To find the biggest possible number of cartons needed, we need to find the greatest common divisor (GCD) of the three numbers: 210, 252, and 294. After all, we want to pack in as many cartons as possible, right? So, let's do some math and find that GCD!
To find the biggest possible number of cartons needed, we need to find the greatest common divisor (GCD) of the three numbers: 210, 252, and 294.
One way to find the GCD is by using prime factorization:
1. Begin by finding the prime factorization of each number:
- 210 = 2^1 * 3^1 * 5^1 * 7^1
- 252 = 2^2 * 3^2 * 7^1
- 294 = 2^1 * 3^1 * 7^2
2. Identify the common prime factors and multiply them together:
- The common prime factors are 2, 3, and 7.
- Multiply these factors: 2 * 3 * 7 = 42
Therefore, the biggest possible number of cartons needed is 42.