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Find the greatest number of children to whom 100 apples, 140 mangoes, and 315 oranges can be divided equally.

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To find the greatest number of children to whom 100 apples, 140 mangoes, and 315 oranges can be equally divided, we need to determine the greatest common divisor (GCD) of the three numbers: 100, 140, and 315.

Here is a step-by-step explanation:

1. Find the GCD of 100 and 140:

- The factors of 100 are: 1, 2, 4, 5, 10, 20, 25, 50, 100.
- The factors of 140 are: 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140.

The common factors of 100 and 140 are: 1, 2, 4, 5, 10, 20.

The greatest common factor among these is 20. Therefore, the GCD of 100 and 140 is 20.

2. Find the GCD of the result from step 1 (which is 20) and 315:

- The factors of 315 are: 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315.

The common factors of 20 and 315 are: 1, 5.

The greatest common factor among these is 5. Therefore, the GCD of 20 and 315 is 5.

Thus, the greatest number of children to whom 100 apples, 140 mangoes, and 315 oranges can be equally divided is 5.

So, each of these 5 children would receive:
- [tex]\( \frac{100}{5} = 20 \)[/tex] apples,
- [tex]\( \frac{140}{5} = 28 \)[/tex] mangoes,
- [tex]\( \frac{315}{5} = 63 \)[/tex] oranges.
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