What is the GCF of 44 and 100?

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gcf, hcf, gcd (44; 100) = ?

The prime factorization of a number: finding the prime numbers that multiply together to make that number.

44 = 22 × 11
44 is not a prime number but a composite one.

100 = 22 × 52
100 is not a prime number but a composite one.

* The natural numbers that are only divisible by 1 and themselves are called prime numbers. A prime number has exactly two factors: 1 and itself.
* A composite number is a natural number that has at least one other factor than 1 and itself.

Multiply all the common prime factors, taken by their smallest powers (exponents).

gcf, hcf, gcd (44; 100) = 22

This algorithm involves the process of dividing numbers and calculating the remainders.

'a' and 'b' are the two natural numbers, 'a' >= 'b'.

Divide 'a' by 'b' and get the remainder of the operation, 'r'.

If 'r' = 0, STOP. 'b' = the gcf (hcf, gcd) of 'a' and 'b'.

Else: Replace ('a' by 'b') and ('b' by 'r'). Return to the step above.

Step 1. Divide the larger number by the smaller one:
100 ÷ 44 = 2 + 12 Step 2. Divide the smaller number by the above operation's remainder:
44 ÷ 12 = 3 + 8 Step 3. Divide the remainder of the step 1 by the remainder of the step 2:
12 ÷ 8 = 1 + 4 Step 4. Divide the remainder of the step 2 by the remainder of the step 3:
8 ÷ 4 = 2 + 0 At this step, the remainder is zero, so we stop: 4 is the number we were looking for - the last non-zero remainder.

This is the greatest (highest) common factor (divisor).

The greatest (highest) common factor (divisor):
gcf, hcf, gcd (44; 100) = 4

Once you've calculated the greatest common factor of the numerator and the denominator of a fraction, it becomes much easier to fully reduce (simplify) the fraction to the lowest terms (the smallest possible numerator and denominator).

Calculate the greatest (highest) common factor (divisor) of numbers, gcd, hcf, gcd:

Method 1: Run the prime factorization of the numbers - then multiply all the common prime factors, taken by their smallest exponents. If there are no common prime factors, then gcf equals 1.

Method 2: The Euclidean Algorithm.

Method 3: The divisibility of the numbers.

• Note 1: The greatest common factor (gcf) is also called the highest common factor (hcf), or the greatest common divisor (gcd).
• Note 2: The Prime Factorization of a number: finding the prime numbers that multiply together to make that number.
• Suppose the number "t" evenly divides the number "a" ( = when evenly dividing the number "a" by "t", the remainder is zero).
• When we look at the prime factorization of "a" and "t", we find that:
• 1) all the prime factors of "t" are also prime factors of "a"
• and
• 2) the exponents of the prime factors of "t" are equal to or smaller than the exponents of the prime factors of "a" (see the * Note below)

• For example, the number 12 is a divisor (a factor) of the number 60:
• 12 = 2 × 2 × 3 = 22 × 3
• 60 = 2 × 2 × 3 × 5 = 22 × 3 × 5
• * Note: 23 = 2 × 2 × 2 = 8. We say that 2 was raised to the power of 3. In this example, 3 is the exponent and 2 is the base. The exponent indicates how many times the base is multiplied by itself. 23 is the power and 8 is the value of the power.

• If the number "t" is a common divisor of the numbers "a" and "b", then:
• 1) "t" only has the prime factors that also intervene in the prime factorization of "a" and "b".
• and
• 2) each prime factor of "t" has the smallest exponents with respect to the prime factors of the numbers "a" and "b".

• For example, the number 12 is the common divisor of the numbers 48 and 360. Below is their prime factorization:
• 12 = 22 × 3
• 48 = 24 × 3
• 360 = 23 × 32 × 5
• You can see that the number 12 has only the prime factors that also occur in the prime factorization of the numbers 48 and 360.
• You can see above that the numbers 48 and 360 have several common factors: 2, 3, 4, 6, 8, 12, 24. Out of these, 24 is the greatest common factor (GCF) of 48 and 360.
• 24 = 2 × 2 × 2 × 3 = 23 × 3
• 48 = 24 × 3
• 360 = 23 × 32 × 5
• 24, the greatest common factor of the numbers 48 and 360, is calculated as the product of all the common prime factors of the two numbers, taken by the smallest exponents (powers).

• If two numbers "a" and "b" have no other common factor than 1, gcf (a, b) = 1, then the numbers "a" and "b" are called coprime numbers (relatively prime, prime to each other).
• If "a" and "b" are not relatively prime numbers, then every common divisor of "a" and "b" is a divisor of the greatest common divisor of "a" and "b".

• Let's have an example on how to calculate the greatest common factor, gcf, of the following numbers:
• 1,260 = 22 × 32
• 3,024 = 24 × 32 × 7
• 5,544 = 23 × 32 × 7 × 11
• gcf (1,260, 3,024, 5,544) = 22 × 32 = 252

• And another example:
• 900 = 22 × 32 × 52
• 270 = 2 × 33 × 5
• 210 = 2 × 3 × 5 × 7
• gcf (900, 270, 210) = 2 × 3 × 5 = 30

• And one more example:
• 90 = 2 × 32 × 5
• 27 = 33
• 22 = 2 × 11
• gcf (90, 27, 22) = 1 - The three numbers have no prime factors in common, they are relatively prime.

What is a prime number? Definition, examples

What is a composite number? Definition, examples

The prime numbers up to 1,000

The prime numbers up to 10,000

The Sieve of Eratosthenes

The Euclidean Algorithm

Completely reduce (simplify) fractions to the lowest terms: Steps and Examples

1. What is the GCF of 100 and 44?

Answer: GCF of 100 and 44 is 4.

2. What are the Factors of 100?

Answer: Factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100. There are 9 integers that are factors of 100. The greatest factor of 100 is 100.

3. What are the Factors of 44?

Answer: Factors of 44 are 1, 2, 4, 11, 22, 44. There are 6 integers that are factors of 44. The greatest factor of 44 is 44.

4. How to Find the GCF of 100 and 44?

Answer:

Greatest Common Factor of 100 and 44 = 4

Step 1: Find the prime factorization of 100

100 = 2 x 2 x 5 x 5

Step 2: Find the prime factorization of 44

44 = 2 x 2 x 11

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

GCF = 2 x 2 = 4

Step 4: Therefore, the greatest common factor of 100 and 44 is 4

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The greatest common factor between them is 4

Given 2 or 3 numbers, the calculator determines the following: * Greatest Common Factor (GCF) using Factor Pairs * Rewrite Sum using the Distributive Property and factoring out the GCF * Least Common Multiple (LCM) / Least Common Denominator (LCD) using Factor Pairs * GCF using the method of Successive Division * GCF using the Prime Factorization method * Determine if the numbers are coprime and twin prime

This calculator has 3 inputs.

divisionseparate a number into partsdivisionseparate a number into partsfactora divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n.greatest common factorlargest positive integer dividing a set of integersgreatest common factor and least common multipleleast common multipleGiven 2 numbers a and b, the least common multiple LCM is the smallest positive integer that is divisible by both. It is commonly denoted as LCM(a, b)minimumthe least or lowest amount possible or attainedmultiplethe product of any quantity and an integernumberan arithmetical value, expressed by a word, symbol, or figure, representing a particular quantity and used in counting and making calculations and for showing order in a series or for identification. A quantity or amount.prime factorizationthe prime numbers that divide that integer exactlyremainderThe portion of a division operation leftover after dividing two integers

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What is the GCF of 44 and 100?

gcf(44, 100) = 4

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GCF of 44 and 101