wikiHow is a wiki, similar to Wikipedia, which means that many of our articles are co-written by multiple authors. The common factors of 20, 50 and 120 are 1, 2, 5 and 10. Greatest Common Factor - Sample Math Practice Problems . In this section, we list the most important ones: If the ratio of two numbers a and b (a > b) is an integer then gcf(a, b) = b. gcf(a, 0) = a, used in Euclidean algorithm. Repeat the game multiple times and estimate what's the percentage of coprime numbers you found. GCF of 42, 42, 76, and 28 = 2. wikiHow is a wiki, similar to Wikipedia, which means that many of our articles are co-written by multiple authors. What level of questions should I make for a test? created an algorithm for finding out what the greatest common factor is in the case of two natural numbers or two polynomials? 16, 28, 56, 112 # Problem Correct Answer Your Answer; 2: 143, 110: Solution The factors of 110 are 1, 2, 5, 10, 11, 22, 55, 110. The whole number factors are numbers that divide evenly into the number with zero remainder. Once the remainder is 0, the GCF is the remainder from the step preceding the zero result. MathWorld--A Wolfram Web Resource. Then, separate the common prime factors of each number and make a list of the common prime factors. Click "Calculate" to see all factors of each number as well as the So, the prime factorization of 104 is, 104 = 2 2 2 13 = 2 3 13. lcm(a, gcf(b, c)) = gcf(lcm(a, b), lcm(a, c)). If you see that your students are very competitive and clever, you can make the test hard, so as to challenge their knowledge about the subject. Maybe you wanted the Least Common Multiple (LCM) Calculator . Accessed 19 January, 2023. Enter values separeted by commas: Procedure to Find the Highest Common Factor of Given Numbers. Continue with Recommended Cookies. It's worth knowing all of them so you can decide which you prefer: The good news is that you can estimate the GCD with simple math operations, without roots or logarithms! Now that we are aware of numerous methods of finding the Greatest Common Divisor of two numbers, you might ask: "how to find the Greatest Common Factor of three or more numbers?". Are you on the hunt for the GCF of 76, 28, and 104? One of these involves computing the prime factorizations of each integer, determining which factors they have in common, and multiplying these factors to find the GCD. Factor each coefficient into primes and write the variables with exponents in expanded form. Let's jump in! The GCF of 21 x 3, 9 x 2 and 15 x is 3 x. This means that we find our Greatest Common Divisor and its value in the penultimate line of the subtractions: 8. For example, 12, 20, and 24 have two common factors: 2 and 4. This method is a far more efficient method than the use of prime factorization. 28 = 2 2 7. Heres how to find the GCF:

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1. Decompose the numbers into their prime factors.

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2. Underline the factors that all the original numbers have in common.

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3. Multiply the underlined numbers to get the GCF.

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Sample questions

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1. Find the greatest common factor of 12 and 20.

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   4. Write down all the factor pairs of 12 and 20:

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   Factor pairs of 12: 1 x 12, 2 x 6, 3 x 4

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   Factor pairs of 20: 1 x 20, 2 x 10, 4 x 5

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   The number 4 is the greatest number that appears in both lists of factor pairs, so its the GCF.

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2. Find the greatest common factor of 24, 36, and 42.

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   6. Decompose all three numbers down to their prime factors:

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   24 = 2 x 2 x 2 x 3

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   36 = 2 x 2 x 3 x 3

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   42 = 2 x 3 x 7

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   Underline all factors that are common to all three numbers:

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   24 = 2 x 2 x 2 x 3

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   36 = 2 x 2 x 3 x 3

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   42 = 2 x 3 x 7

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   Multiply those underlined numbers to get your answer:

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   2 x 3 = 6

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Practice questions

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1. Find the greatest common factor of 10 and 22.

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2. Whats the GCF of 8 and 32?

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3. Find the GCF of 30 and 45.

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4. Figure out the GCF of 27 and 72.

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5. Find the GCF of 15, 20, and 35.

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6. Figure out the GCF of 44, 56, and 72.

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Following are the answers to the practice questions:

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1. The GCF of 10 and 22 is 2.

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   Write down all the factor pairs of 10 and 22:

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   10: 1 x 10, 2 x 5

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   22: 1 x 22, 2 x 11

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   The number 2 is the greatest number that appears on both lists.

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2. The GCF of 8 and 32 is 8.

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   Write down all the factor pairs of 8 and 32:

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   8: 1 x 8, 2 x 4

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   32: 1 x 32, 2 x 16, 4 x 8

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   The greatest number that appears on both lists is 8.

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3. The GCF of 30 and 45 is 15.

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   Write down all the factor pairs of 30 and 45:

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   30: 1 x 30, 2 x 15, 3 x 10, 5 x 6

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   45: 1 x 45, 3 x 15, 5 x 9

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   The greatest number that appears on both lists is 15.

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4. The GCF of 27 and 72 is 9.

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   Decompose 27 and 72 into their prime factors and underline every factor thats common to both:

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   27 = 3 x 3 x 3

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   72 = 2 x 2 x 2 x 3 x 3

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   Multiply those underlined numbers to get your answer: 3 x 3 = 9.

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5. The GCF of 15, 20, and 35 is 5.

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   Decompose the three numbers into their prime factors and underline every factor thats common to all three:

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   15 = 3 x 5

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   20 = 2 x 2 x 5

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   35 = 5 x 7

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   The only factor common to all three numbers is 5.

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6. The GCF of 44, 56, and 72 is 4.

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   Decompose all three numbers to their prime factors and underline each factor thats common to all three:

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   44 = 2 x 2 x 11

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   56 = 2 x 2 x 2 x 7

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   72 = 2 x 2 x 2 x 3 x 3

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   Multiply those underlined numbers to get your answer: 2 x 2 = 4.

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","blurb":"","authors":[{"authorId":9399,"name":"Mark Zegarelli","slug":"mark-zegarelli","description":" Mark Zegarelli is a professional writer with degrees in both English and Math from Rutgers University. List of positive integer factors of 104 that divides 91 without a remainder. It can also be referred to as a common divisor. Consider the factors of 27, 54, and 81: Each of the numbers can be divided by 1, 3, 9, and 27, so you can say that these numbers are common factors of the set of numbers 27, 54, and 81. 76 1, 2, 4, 19, 38, 76. [2] 2. You can do that by encircling each common factor or drawing a line segment between them. Find the prime factorization of 16. Show Work? For most cases they are just subtraction, multiplication, or division. Hopefully you've learned a little math today and understand how to calculate the GCD of numbers. The procedure to find the HCF of number by division method is as follows: Find the HCF of 30 and 42 using the Division method? The lowest y exponent is also 1. Make use of the HCF Calculator provided here and calculate the highest common factor for the given numbers. HCF Calculator: Finding the Highest Common Factor is similar to the Greatest common factor or divisor as HCF is also known as GCF or GCD. GCF of our third value, 20, and our result, 10. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/6\/6b\/Find-the-Greatest-Common-Factor-Step-1-Version-2.jpg\/v4-460px-Find-the-Greatest-Common-Factor-Step-1-Version-2.jpg","bigUrl":"\/images\/thumb\/6\/6b\/Find-the-Greatest-Common-Factor-Step-1-Version-2.jpg\/aid1798549-v4-728px-Find-the-Greatest-Common-Factor-Step-1-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"