Question

a 2×2 grid (table) with numbers 49 (bottom - left cell), 42 (bottom - right cell), 24 (top - right cell), and the top - left cell blank. vertical and horizontal lines frame the grid.

Explanation:

Step1: Find the GCD of 49 and 42

First, we find the greatest common divisor (GCD) of 49 and 42. The factors of 49 are 1, 7, 49. The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42. The common factor is 7. So, GCD(49, 42) = 7.

Step2: Find the missing number

Now, we know that in a grid like this (probably a multiplication or division grid), the relationship between the numbers. Let's assume the missing number is \( x \). We can see that 42 and 24 might have a similar relationship with their corresponding numbers. Wait, maybe it's a ratio. Let's check the ratio of 49 to 42, which is \( \frac{49}{42}=\frac{7}{6} \). So, if we apply the same ratio to 24, we get \( x = 24\times\frac{7}{6} \).

Calculating \( 24\times\frac{7}{6} \): \( 24\div6 = 4 \), then \( 4\times7 = 28 \). Wait, or maybe the other way. Wait, 42 divided by 24 is \( \frac{42}{24}=\frac{7}{4} \)? No, that doesn't match. Wait, maybe it's a factor. Wait, 49 is 7×7, 42 is 7×6. So the first column is 7×7 and 7×6. Then the second column: 24 is 4×6, so the missing number should be 4×7 = 28. Let's verify. 49 (7×7) and 28 (4×7) in the first row? Wait, no, the grid is two rows and two columns. First row: \( x \) and 24. Second row: 49 and 42. So the ratio of the second row is 49:42 = 7:6. So the first row should also be in 7:6 ratio. So \( x:24 = 7:6 \). Cross - multiplying, \( 6x = 24\times7 \), \( 6x = 168 \), \( x=\frac{168}{6}=28 \).

Answer:

28