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What method do you like best for gcf why?
This answer is in the context of numbers that are likely to crop up in school or graduate mathematics, not in cryptology or advanced research. Complete factorisation of large numbers is tedious and may require a lot of false starts (if the next factor is quite large). So, for large numbers I would start with Euclid's algorithm (see link). All that is required for this process is subtraction. The problem of finding the GCF of two large numbers soon becomes that of finding the GCF of two very much smaller numbers. Although the method can be carried out to the end, I will often choose to switch to factorisation when the numbers are smaller: below 400, say, when all you need to know is the times tables to 20. Given all the divisibility rules, this is not as daunting as it may sound.
Is this true or false ' if 2 numbers are each divisible by another number then their difference is also divisible by that number'?
True, and this property is useful for finding the greatest common factor (GCF) of two (or more) large numbers.If A > B, then GCF(A , B) = GCF(A - B, B) where A - B is smaller than A.Repeat, each time subtracting the smaller number from the bigger.Keep going until both numbers in the parentheses are the same: that number is the GCF of A and B.GCF by subtraction rather than factorising or division. Unfortunately, it can be quite slow. You could speed it up by doing A - 2B or A - 3B etc rather than A - B.True, and this property is useful for finding the greatest common factor (GCF) of two (or more) large numbers.If A > B, then GCF(A , B) = GCF(A - B, B) where A - B is smaller than A.Repeat, each time subtracting the smaller number from the bigger.Keep going until both numbers in the parentheses are the same: that number is the GCF of A and B.GCF by subtraction rather than factorising or division. Unfortunately, it can be quite slow. You could speed it up by doing A - 2B or A - 3B etc rather than A - B.True, and this property is useful for finding the greatest common factor (GCF) of two (or more) large numbers.If A > B, then GCF(A , B) = GCF(A - B, B) where A - B is smaller than A.Repeat, each time subtracting the smaller number from the bigger.Keep going until both numbers in the parentheses are the same: that number is the GCF of A and B.GCF by subtraction rather than factorising or division. Unfortunately, it can be quite slow. You could speed it up by doing A - 2B or A - 3B etc rather than A - B.True, and this property is useful for finding the greatest common factor (GCF) of two (or more) large numbers.If A > B, then GCF(A , B) = GCF(A - B, B) where A - B is smaller than A.Repeat, each time subtracting the smaller number from the bigger.Keep going until both numbers in the parentheses are the same: that number is the GCF of A and B.GCF by subtraction rather than factorising or division. Unfortunately, it can be quite slow. You could speed it up by doing A - 2B or A - 3B etc rather than A - B.
What is the GCF of the numbers 141 and 192?
The GCF is 3.
What is the GCF of the numbers 40 and 64?
The GCF is 8.
What is the GCF of the numbers 125 and 50?
The GCF is 25.
When do you use GCF and LCM?
Gcf you use when you are finding the greatest factor for the numbers. Lcm you use when you are finding the smallest multiple in the numbers factors
How do you use the greatest common factor subtraction method?
If you have two numbers A and B, and A > B, then GCF(A, B) = (A-B, B) Thus the problem of finding the GCF of A and B has been reduced to finding the GCF of B and a smaller number, A-B. This process can be continued until the two numbers are the same: and that number is the GCF.
How can you find the GCF of a given set of numbers given their LCM but without listing the factors of the numbers?
By finding their common prime numbers.
What method do you like best for gcf why?
This answer is in the context of numbers that are likely to crop up in school or graduate mathematics, not in cryptology or advanced research. Complete factorisation of large numbers is tedious and may require a lot of false starts (if the next factor is quite large). So, for large numbers I would start with Euclid's algorithm (see link). All that is required for this process is subtraction. The problem of finding the GCF of two large numbers soon becomes that of finding the GCF of two very much smaller numbers. Although the method can be carried out to the end, I will often choose to switch to factorisation when the numbers are smaller: below 400, say, when all you need to know is the times tables to 20. Given all the divisibility rules, this is not as daunting as it may sound.
What does greatest common factor do?
The GCF is the largest number common to a given set of two or more numbers. Finding the GCF helps you to reduce fractions.
How Given any two numbers which is greater the LCM of the numbers or. The GCF of the numbers why?
The LCM will never be less than the GCF. To be a multiple of both numbers, the LCM will have to be equal to or greater than the larger number. To be a factor of both numbers, the GCF will have to be equal to or less than the smaller number. The only problem comes when you're comparing a number to itself. The LCM of 10 and 10 is 10. The GCF of 10 and 10 is 10.
What is the gcf of the numerator and denominator?
The greatest common factor, or GCF, is the largest positive integer that will divide evenly with no remainder into all the members of a given set of numbers. When those numbers are a numerator and a denominator, finding the GCF will tell you if the fraction is in its simplest form.
Why is it important to find the greatest common factor?
Because some numbers have a lot of factors. Consider 2520. The factor pairs (2520,1)(504,5)(360,7)(315,8)(280,9)(72,35)(63,40)(56,45) all are relatively prime, which means that they have a GCF of 1. Whenever a pair of numbers has a GCF of 1, the LCM is their product, which in this case is 2520. So here are 8 distinct sets of numbers with the same GCF and LCM. It happens more frequently the more factors you have.
What is a shortcut for GCF?
Example: 30 and 42Factor them.2 x 3 x 5 = 302 x 3 x 7 = 42Select the common factors.2 x 3 = 6, the GCF
What are the three methods for finding the gcf of 10?
You need at least two numbers to find a GCF.
How can you find the gcf of two numbers without knowing the factors?
If one of the numbers is a multiple of the other, the smaller number is the GCF. If the two numbers are prime numbers, the GCF is 1. If the numbers are consecutive, the GCF is 1. If the numbers are consecutive even numbers, the GCF is 2.
How do you find a pair of numbers when the GCF is given?
To find a pair of numbers with a given GCF, take the GCF number and double it. The pair of numbers is the GCF, and two times the GCF. For instance, two numbers with a GCF of 3 are 3 and 6.
