What is the GCF of 27 and 45?
The largest possible number which divides the given numbers exactly without any remainder is called as its Greatest Common Factor
Answer: GCF of 27 and 45 is 9
The GCF (greatest common factor) is the same as: HCF (Highest Common Factor), GCD (Greatest Common Divisor), HCD (Highest Common Divisor), GCM (Greatest Common Measure), HCM (Highest Common Measure)
Two methods to find the GCF of 27 and 45 are explained below.
Methods to find GCF of 27 and 45
- GCF of 27 and 45 by Prime Factorization
- GCF of 27 and 45 by Long Division
Method 1: Prime Factorization to Obtain GCF of 27 and 45
Let us represent 27 and 45 as a product of its prime factors.
Prime factorization of 27 is 3 × 3 × 3
Prime factorization of 45 is 3 × 3 × 5
Common factors = 3 and 3
GCF is the product of the factors that are common to each of the given numbers.
GCF is 9
Method 2: Long Division to Obtain GCF of 27 and 45
- Step 1: Divide 45(number which is larger) by 27(number which is smaller) and check the remainder.
- Step 2: Make the remainder of the above step as the divisor and the divisor of the above step as the dividend and perform the long division again.
- Step 3: Continue the division till you get remainder as zero.
By both the methods we arrive at the same answer.