What is the highest common factor of 21 and 35?

Answer 1

The greatest common factor (GCF) is often also called the greatest common divisor (GCD) or highest common factor (HCF). Keep in mind that these different terms all refer to the same thing: the largest integer which evenly divides two or more numbers.

The greatest common factor of 35 and 210 is 35

Answer 2

There are two popular methods to answer greatest common factor questions. The traditial method has to do with listing all the factors of each number. This can take a long time and become very tasking.

The method I will show you for this problem is using the prime factors each number has in common.

Steps:

1. First use a tree diagram to find the prime factorization of each number.

Prime factorization for 35: 5*7

Prime factorization for 225: 3*3*5*5

2. Find the prime factors that each number has in common. For this problem they only have on pair of prime factors which is 5. Since there is only one pair, 5 is the GCF (greatest common factor).

3. In other situations where there are more than one pair of prime factors, multiply them together. For example, the pairs of common prime factors from 225 and 750 are 3, 5, and 5. So the GCF of 225 and 750 will be 75 as a result of multiplying 3*5*5.

Answer 3

The GCF is 7.

Answer 4

The GCF is 7.
GCF(21, 35) = 7

Answer 5

HCF(21, 35) = 7