What is the gcf of 26 and 65?
GCF of a set of whole numbers is the largest positive integer (i.e whole number and not a decimal) that divides evenly into all of the numbers in the set.
Answer: The GCF of 26 and 65 is 13
Let us see how to find the GCF of 26 and 65
Let us find the GCF using 2 methods
- Long division
- Prime factorization
Method 1 : GCF (26,63) by Prime factorization
To calculate the GCF of 26 and 65 lets's decompose them into their respective prime factors as shown below
we see that the common factors of 26 and 65 is 13
Hence, GCF of 26 and 65 = 13
Method 2: GCF(26,65) by Long Division
We will now be looking into another method to calculate the GCF using long division method.
- Divide the largest number by the smallest number. i.e, 65 divided by 26
- Take divisor as new dividend and remainder as the new divisor, i.e. divide the first divisor by the first remainder.
- Proceed till the remainder is zero and the last divisor will be the GCF of the given numbers.