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What is the greatest common multiple of 100 and 140?
No two numbers can have a greatest common multiple. For, suppose x is the greatest common multiple of two numbers, a and b. That means x = m*a and x = n*b where m and n are some positive integers. Then any multiple of x, say p*x where p is an integer, will be a multiple of a and b because p*x = p*(m*a) = (p*m)*a p*y = p*(n*b) = (p*n)*b m,n,p are integers so p*m and p*n are integers and p*x > x So p*x is a common multiple, and is greater than x, contradicting the assumption that x is the greatest.
What is factor theorem?
x-a is a factor of the polynomial p(x),if p(a)=0.also,if x-a is a factor of p(x), p(a)=0.
How can you write equivalent expressions with Greatest common factor and the distributive property?
Suppose x and y are two terms with GCF k where the assumption (in this context) is that k is greater than 1. That implies that x = pk and y = qk where p and q are coprime terms. Then x + y = pk + qk and, using the distributive property, this is k*(p + q).
What 2 numbers have the greatest common factor of 10?
There are infinitely many possible answers. There are infinitely many prime numbers. Suppose p and q are any two primes. Then the GCF of 10p and 10q is 10. In fact, p and q don't even have to be prime numbers: being relatively prime is sufficient (and necessary).
How can you get an equivalent fraction?
With a given fraction N/D, where N & D are integers [D not equal to zero]. Take any nonzero integer (p). Multiply both N and D by p:N/D = (N*p)/(D*p)Also, if N & D have any common factors {call it q}, then dividing N & D by q will give an equivalent fraction. So if the fraction is 6/16, let p = 3: the new fraction is 18/48. Since 6 and 16 have a common factor of 2, you can divide both 6 & 16 by 2 and get 3/8, which is equivalent to 6/16 and 18/48.Here are some more examples: a fraction equivalent to 1/2 would be 7/14. to reduce a fraction, find the Greatest Common Factor between the two sides. for example, if you were reducing 36/60, the greatest common factor between 36 and 60 would be 12. 36 divided by 12 is 3, and 60 divided by 12 is 5. so, a fraction equivalent to 36/60 would be 3/5. 3 and 5 cannot reduce any further.
What is the greatest common factor of 5p?
There is not a greatest common factor of a single number, such as 5p, because there cannot be a greatest common factor without two or more numbers to compare. Common factors are factors that the numbers being compared have in common. The greatest common factor is the largest factor that all the numbers being compared have in common. Thus, since there are not two or more numbers to compare, there are neither common factors nor a greatest common factor.The factors of 5p are 1, 5, p, and 5p.Examples:The greatest common factor of 5p and 30p is 5p.The greatest common factor of 5p and 43p is p.The greatest common factor of 5p and 83 is 1, unless p is a multiple of 83, in which case the greatest common factor is 83.
What is the greatest common factor of 27pq 8p 15p?
Just p.
What is the greatest common factor of 5p and 20p 2?
The greatest common factor (GCF) of 5p and 20pĀ² is 5p. To find the GCF, you need to identify the common factors of both terms and choose the highest one. In this case, both terms have 5 and p as common factors, but the term with the lower power of p is 5p. Therefore, the GCF is 5p.
Greatest common factor of 49 and 144?
I think its 7 im not sure llook on google its a better place sort of :p
What is the greatest common factor of 12p squared and 30q to the 5th power?
Since the p and the q have nothing in common, the common factor will just be for the coefficients (number part of the terms). The prime factors (from a factor tree) of 12 are 2 x 2 x 3, and those of 30 are 2 x 3 x 5. The only ones they both have in common are 2 and 3, so we multiply these and get the greatest common factor of 6.
Why is the gcf of two even numbers are always even?
All even numbers have two as a factor. That means that any set of even numbers will have at least a two as a common factor. Since 2 will be a part of the greatest common factor, it will have to be even.
What is the greatest common multiple of 100 and 140?
No two numbers can have a greatest common multiple. For, suppose x is the greatest common multiple of two numbers, a and b. That means x = m*a and x = n*b where m and n are some positive integers. Then any multiple of x, say p*x where p is an integer, will be a multiple of a and b because p*x = p*(m*a) = (p*m)*a p*y = p*(n*b) = (p*n)*b m,n,p are integers so p*m and p*n are integers and p*x > x So p*x is a common multiple, and is greater than x, contradicting the assumption that x is the greatest.
What is the greatest common factor of 9 and 16?
The GCF of 9 and 16 is 1 because it is the only factor shared by both numbers, and thus is the greatest.The p rime factorization of 9 = 3x3The prime factorization of 16 = 2x2x2x2Nothing is common from the prime factorization of both numbers.Therefore, Greatest Common Factor is 1.The greatest common factor of 9 and 16 is 1.
How do you use a factor tree to find the greatest common factor?
Factor trees are used to determine the prime factors of a number. When you have the prime factors of each of the numbers you are comparing, find out which prime factors they have in common. When you have the prime factors that they all have in common, multiply those prime factors together. This number will be the greatest common factor. Example: Find the greatest common factor of 18 and 54. 18 3 x 6 3 x (2x3) The prime factors of 18 are 2, 3, and 3. 54 6 x 9 (2x3) x (3x3) The prime factors of 54 are 2, 3, 3, and 3. The prime factors that 18 and 54 have in common are 2, 3 and 3, so the greatest common factor is 2 x 3 x 3 = 18. Example: Find the greatest common factor of 24 and 52. 24 4 x 6 (2x2) x (2x3) The prime factors of 24 are 2, 2, 2, and 3. 52 2 x 26 2 x (2x13) The prime factors of 52 are 2, 2, and 13. The prime factors that 24 and 52 have in common are 2 and 2, so the greatest common factor is 2 x 2 = 4. Make a factor tree for the first number and when you are finished reducing the number to its prime factors, put them in order. Then, do the same with the other number. Put the two lists of prime factors in two rows, so you can compare them, like this: 12 = 2 x 2 x 3 8= 2 x 2 x 2 After that, line them up to determine which ones match. They both have two 2s, but nothing else is the same, so multiply both together 2 x 2 = 4 to get the greatest common factor. 4 is the Greatest Common Factor (GCF) Hope it helps, Sakura They don't have to align vertically. E.g.: 6 = 2 x 3 15= 3 x 5 GCF=3 (since each of the numbers has a factor of 3). Basically, for each prime number p, you check how many times p appears in each of the two numbers, and then take the minimum. In this case: 2 occurs 1 time in 6 and 0 times in 15; the minimum of 1 and 0 is 0; therefore 2 occurs 0 times in the GCF. You do this for each of the primes, and get 3.
What are the 2 numbers between 35 and 46 that are the greatest common factors?
Each and every one of them.If p and q are any two primes and if k is any number between 35 and 46, thenk will be the greatest common factor of p*k and q*k.
What is the greatest common factor of 21 p2q and 35pq2?
When 'p' and 'q' are both greater than '1', it's 7pq .When either of them is less than '1', no telling.
How do you factorize p plus prt?
The only common factor of the two expressions is p Then p + prt = p(1 + rt)
