Question

What is the GCF of 35 and 49?

Answer 1

`7`

Explanation:

One simple but sometimes slow method for finding the GCF of two positive numbers goes as follows:

• If the two numbers are equal then they are equal to the GCF.

• Otherwise replace the larger number with the result of subtracting the smaller number from it.

In our example:

• Start with `35` and `49`

• Since they are unequal, subtract `35` from `49`, getting `14`

• Our two numbers `35` and `14` are unequal, so replace `35` with `35-14 = 21`.

• `21` and `14` are unequal, so replace `21` with `21-14 = 7`.

• `14` and `7` are unequal, so replace `14` with `14-7 = 7`.

• `7` and `7` are equal, so they are our GCF.