What is the GCF of 27 and 30?
GCF (Greatest Common Factor) of two numbers is the largest possible number that divides the two numbers exactly without leaving any remainder.
Answer: GCF of 27 and 30 is 3
GCF of 27 and 30 is the highest number that divides 27 and 30 exactly leaving the remainder 0.
We can find the GCF of 27 and 30 by the following two methods.
- Prime factorization Method
- Long division Method
Method 1: GCF of 27 and 30 by Prime Factorization
Let us represent 27 and 30 as a product of its prime numbers
Prime factorization of 27 is 3 × 3 × 3
Prime factorization of 30 is 2 × 3 × 5
3 is the only common factor in the prime factorization of 27 and 30
GCF of 27 and 30 is the product of the prime factors that are common to each of the given numbers.
GCF of 27 and 30 is 3.
Method 2: GCF of 27 and 30 by Long Division
Step 1: Divide the largest number 30 by the smaller number 27 and check the remainder. Here, the remainder is 3
Step 2: Make the remainder 3 as the divisor and the divisor 27 as the dividend and perform the long division again.
Step 3: Continue till you get the remainder as 0 and GCF of 27 and 30 is the last divisor obtained.
You can find the GCF in any of the above methods but the solution will be the same.