Greatest Common Divisor (GCD) of 7, 10, and 12

In this article we will calculate and work out the Greatest Common Divisor (GCD) of the numbers 7, 10, and 12.

The GCD of 7, 10, and 12 is the largest positive integer (a whole number with no decimal) that can be divided evenly into all of the numbers in the set.

You might have seen this called the Greatest Common Factor (GCF) or the Highest Common Factor (HCF). They all mean the same thing.

If you are calculating the Greatest Common Divisor of 7, 10, and 12 yourself, the easiest way to do that might be to actually list out all of the divisors for each number and then find out what the greatest common divisor is.

For 7, 10, and 12 those divisors look like this:

  • Divisors for 7: 1 and 7
  • Divisors for 10: 1, 2, 5, and 10
  • Divisors for 12: 1, 2, 3, 4, 6, and 12

As you can see when you list out the divisors of each number, 1 is the greatest number that 7, 10, and 12 divides into.

When working with larger numbers, though, listing through all of the divisors will take a lot of computer processing power.

When working with larger numbers, or even with smaller numbers when you want to find the Greatest Common Divisor of 7, 10, and 12 in the most efficient way possible, we would use Prime Factors.

A Prime Number is one that is divisible only by itself and the number 1. And so a Prime Factor is a Prime Number which is also a Factor of 7, 10, and 12.

The algorithm I use for this is much more efficient because there are far less Prime Factors in 7, 10, and 12.

For 7, 10, and 12 the Prime Factors are:

  • Prime Factors for 7: 7
  • Prime Factors for 10: 2 and 5
  • Prime Factors for 12: 2 and 3

You can see again from the bolded number 1 that the Greatest Common Divisor of 7, 10, and 12 is 1.

GCD(7,10,12) = 1

Hopefully I have been able to explain the GCD of 7, 10, and 12 and given you some information that you can use to try this for yourself and calculate the Greatest Common Divisor of a new set of numbers.

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