GCF of 105 and 189 (Greatest Common Factor)

"Greatest Common Factor" Calculator

What is the Greatest Common Divisor of 105 and 189?

Answer

GCF of 105 and 189 is

(Twenty-one)

Finding GCF for 105 and 189 using all factors (divisors) listing

The first method to find GCF for numbers 105 and 189 is to list all factors for both numbers and pick the highest common one:

All factors of 105: 1, 3, 5, 7, 15, 21, 35, 105

All factors of 189: 1, 3, 7, 9, 21, 27, 63, 189

So the Greatest Common Factor for 105 and 189 is 21

Finding GCF for 105 and 189 by Prime Factorization

The second method to find GCF for numbers 105 and 189 is to list all Prime Factors for both numbers and multiply the common ones:

All Prime Factors of 105: 3, 5, 7

All Prime Factors of 189: 3, 3, 3, 7

As we can see there are Prime Factors common to both numbers: 3, 7

Now we need to multiply them to find GCF: 3 × 7 = 21

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About "Greatest Common Factor" Calculator

This calculator will help you find the greatest common factor (GCF) of two numbers. For example, it can help you find out what is the Greatest Common Divisor of 105 and 189? (The answer is: 21). Select the first number (e.g. '105') and the second number (e.g. '189'). After that hit the 'Calculate' button.

Greatest Common Factor (GCF) also known as the Greatest Common Divisor (GCD) or Highest Common Factor (HCF) - it is the largest positive integer that divides each of the integers with zero remainder.

"Greatest Common Factor" Calculator

GCF Table

Number 1	Number 2	GCF
105	174	3
105	175	35
105	176	1
105	177	3
105	178	1
105	179	1
105	180	15
105	181	1
105	182	7
105	183	3
105	184	1
105	185	5
105	186	3
105	187	1
105	188	1
105	189	21
105	190	5
105	191	1
105	192	3
105	193	1
105	194	1
105	195	15
105	196	7
105	197	1
105	198	3
105	199	1
105	200	5
105	201	3
105	202	1
105	203	7

FAQ

What is the Greatest Common Divisor of 105 and 189?

GCF of 105 and 189 is 21

How to find the GCF of 105 and 189?

You can find the GCF of 105 and 189 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 105 and 189 is 21.

What prime factors do 105 and 189 share?

The prime factorizations of 105 and 189 have 3 × 7 in common, and multiplying those shared primes gives 21 — exactly the greatest common factor.

How does the GCF reduce the fraction 105/189?

Divide the numerator and the denominator by the GCF 21: 105 ÷ 21 = 5 and 189 ÷ 21 = 9. So 105/189 in lowest terms is 5/9.

GCF of 105 and 189 (Greatest Common Factor)

What is the Greatest Common Divisor of 105 and 189?

Finding GCF for 105 and 189 using all factors (divisors) listing

Finding GCF for 105 and 189 by Prime Factorization

Related Calculations

See Also

About "Greatest Common Factor" Calculator

GCF Table

FAQ

What is the Greatest Common Divisor of 105 and 189?

How to find the GCF of 105 and 189?

What prime factors do 105 and 189 share?

How does the GCF reduce the fraction 105/189?

See Also

Number 1	Number 2	GCF
105	174	3
105	175	35
105	176	1
105	177	3
105	178	1
105	179	1
105	180	15
105	181	1
105	182	7
105	183	3
105	184	1
105	185	5
105	186	3
105	187	1
105	188	1
105	189	21
105	190	5
105	191	1
105	192	3
105	193	1
105	194	1
105	195	15
105	196	7
105	197	1
105	198	3
105	199	1
105	200	5
105	201	3
105	202	1
105	203	7

Number 1	Number 2	GCF
105	174	3
105	175	35
105	176	1
105	177	3
105	178	1
105	179	1
105	180	15
105	181	1
105	182	7
105	183	3
105	184	1
105	185	5
105	186	3
105	187	1
105	188	1
105	189	21
105	190	5
105	191	1
105	192	3
105	193	1
105	194	1
105	195	15
105	196	7
105	197	1
105	198	3
105	199	1
105	200	5
105	201	3
105	202	1
105	203	7

Number 1	Number 2	GCF
105	174	3
105	175	35
105	176	1
105	177	3
105	178	1
105	179	1
105	180	15
105	181	1
105	182	7
105	183	3
105	184	1
105	185	5
105	186	3
105	187	1
105	188	1
105	189	21
105	190	5
105	191	1
105	192	3
105	193	1
105	194	1
105	195	15
105	196	7
105	197	1
105	198	3
105	199	1
105	200	5
105	201	3
105	202	1
105	203	7