Final answer:
The GCF between 24 and 36 is 12, so 12 students can be invited to the picnic and share the food equally.
Step-by-step explanation:
To determine how many students can be invited to the picnic and share the food equally, we need to find the factors of both 24 and 36 and choose the greatest common factor (GCF) between them.
The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
The GCF between 24 and 36 is 12. Therefore, 12 students can be invited to the picnic and share the food equally.