Find the highest common factor of $$1680 and $$7350.

Sure, here are the steps to find the highest common factor (HCF) of 1680 and 7350:

Step 1: Prime factorization of the numbers

• Prime factorization of 1680 = 2^4 * 3 * 5 * 7
• Prime factorization of 7350 = 2 * 3^2 * 5^2 * 7

Step 2: Identify the common factors The common factors are 2, 3, 5, and 7.

Step 3: Choose the lowest power of each common factor

• The lowest power of 2 is 2^1.
• The lowest power of 3 is 3^1.
• The lowest power of 5 is 5^1.
• The lowest power of 7 is 7^1.

Step 4: Multiply the common factors raised to the lowest power

• HCF = 2^1 * 3^1 * 5^1 * 7^1 = 2 * 3 * 5 * 7 = 210

So, the highest common factor of 1680 and 7350 is 210.