What is the greatest common factor of 35 and 28

Prime Factorization of 28

Prime factors of 28 are 2,7. Prime factorization of 28 in exponential form is:

28 = 22×71

Prime Factorization of 35

Prime factors of 35 are 5,7. Prime factorization of 35 in exponential form is:

35 = 51×71

∴ So by taking common prime factors GCF of 28 and 35 is 7

Factors of 28

List of positive integer factors of 28 that divides 28 without a remainder.

1,2,4,7,14,28

Factors of 35

List of positive integer factors of 35 that divides 35 without a remainder.

1,5,7,35

Greatest Common Factor

We found the factors and prime factorization of 28 and 35. The biggest common factor number is the GCF number.
So the greatest common factor 28 and 35 is 7.

Also check out the Least Common Multiple of 28 and 35

(i) The GCF of 28 and 35 is associative

GCF of 28 and 35 = GCF of 35 and 28

1. What is the GCF of 28 and 35?

Answer: GCF of 28 and 35 is 7.

2. What are the Factors of 28?

Answer: Factors of 28 are 1, 2, 4, 7, 14, 28. There are 6 integers that are factors of 28. The greatest factor of 28 is 28.

3. What are the Factors of 35?

Answer: Factors of 35 are 1, 5, 7, 35. There are 4 integers that are factors of 35. The greatest factor of 35 is 35.

4. How to Find the GCF of 28 and 35?

Answer:

Greatest Common Factor of 28 and 35 = 7

Step 1: Find the prime factorization of 28

28 = 2 x 2 x 7

Step 2: Find the prime factorization of 35

35 = 5 x 7

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = 7

Step 4: Therefore, the greatest common factor of 28 and 35 is 7

See a solution process below:

Explanation:

Find the prime factors for each number as:

#35 = 5 xx 7#

#28 = 2 xx 2 xx 7#

Now identify the common factors and determine the GCF:

#35 = 5 xx color(red)(7)#

#28 = 2 xx 2 xx color(red)(7)#

Therefore:

#"GCF" = color(red)(7)#

The first step to this method of finding the Greatest Common Factor of 28 and 35 is to find and list all the factors of each number. Again, you can see how this is done by looking at the “Factors of” articles that are linked to above.

Let’s take a look at the factors for each of these numbers, 28 and 35:

Factors of 28: 1, 2, 4, 7, 14, 28

Factors of 35: 1, 5, 7, 35

When you compare the two lists of factors, you can see that the common factor(s) are 1, 7. Since 7 is the largest of these common factors, the GCF of 28 and 35 would be 7.

Greatest Common Factor Calculator / Converter

You have reached us maybe looking for answers to the questions like: What is the greatest common factor of 28 and 35? or what is the highest common factor (HCF) of 28 and 35?

What is the GCF of 28 and 35?

The first step to find the gcf of 28 and 35 is to list the factors of each number. The factors of 28 are 1, 2, 4, 7, 14 and 28. The factors of 35 are 1, 5, 7 and 35. So, the Greatest Common Factor for these numbers is 7 because it divides all them without a remainder. Read more about Common Factors below.

See also:

• Least Common Multiplier (LCM) Calculator
• Fraction Calculator
• Equivalent Fractions Calculator

How to find the Greatest Common Factor

GCF example:

The first step is to find all divisors of each number. For instance, let us find the gcf(28, 35).

In this case we have:

• The factors of 28 (all the whole numbers that can divide the number without a remainder) are 1, 2, 4, 7, 14 and 28;
• The factors of 35 are 1, 5, 7 and 35.

The second step is to analyze which are the common divisors. It is not difficult to see that the 'Greatest Common Factor' or 'Divisor' for 28 and 35 is 7. The GCF is the largest common positive integer that divides all the numbers (28, 35) without a remainder.

In the name greatest common divisor, the adjective "greatest" may be replaced by "highest", and the word "divisor" may be replaced by "factor", so that other names include highest common factor (hcf), greatest common measure, among others.

So, the GCF is also known as:

• Greatest common divisor (gcd);
• Highest common factor (hcf);
• Greatest common measure (gcm), or
• Highest common divisor

Greatest Common Factor Calculator

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