The numbers p and a written as the products of their prime factors arep= 2^4 ×3^3 x7 and g= 2^2 x7^2 x11^6Find the greatest whole number that will divide both p and g exactly

To find the greatest whole number that will divide both p and g exactly, we need to find the common prime factors of p and g.

The prime factors of p are 2, 3, and 7. The prime factors of g are 2, 7, and 11.

To find the common prime factors, we take the smallest exponent for each prime factor:

• The exponent of 2 in p is 4, and the exponent of 2 in g is 2. So, the common exponent of 2 is 2.
• The exponent of 7 in p is 1, and the exponent of 7 in g is 2. So, the common exponent of 7 is 1.

Therefore, the greatest whole number that will divide both p and g exactly is 2^2 x 7^1 = 4 x 7 = 28