Question

What is the greatest common factor shared by 70 and 80?

Answer 1

Greatest Common Factor is `10`

Explanation:

Factors of `70` are `{color(red)(1,2,5),7,color(red)10,14,35,70}`

Factors of `80` are `{color(red)(1,2),4,color(red)5,8,color(red)10,16,20,40,80}`

Common Factors are `{color(red)(1,2,5),color(blue)10}`

and Greatest Common Factor is `10`

Answer 2

`10`

Explanation:

One method of finding the greatest common factor (GCF) of two numbers goes as follows:

• Divide the larger number by the smaller to give a quotient and remainder.

• If the remainder is `0` then the smaller number is the GCF.

• Otherwise repeat with the smaller number and remainder.

So given `70` and `80` we would proceed as follows:

`80 / 70 = 1" "` with remainder `10`

`70 / 10 = 7" "` with remainder `0`

So the GCF of `70` and `80` is `10`

Answer 3

`HCF = 2 xx5 =10`

Explanation:

Write each number as the product of its prime factors.. Then we know what we are dealing with.

`color(white)(xxxx)70 = 2color(white)(xxx.xx)xx5xx7`
`color(white)(xxxx)80 = 2xx2xx2xx5`

`HCF = color(white)(xx)2color(white)(xxxx.x) xx 5 = 10`

From this it is clear that 70 and 80 have 2 common factors - 2 and 5.

The Highest Common Factor is the product of any common factors.

If we write the factors in index form we have exactly the same format that is used with variables in algebra.

`70 = (2)(5)(7) = 2*5*7`
`80 = (2^3)(5) = 2^3*5`

The`HCF = 2xx5 = 10`

From this format we can determine the LCM with no extra working.

The `LCM = 2^3 xx5 xx7 = 280`