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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.
