Tutor profile: Jason H.
Subject: Basic Math
Find the greatest common factor of 400, 288, and 504.
The first step in finding the greatest common factor is factoring each number until only prime numbers remain (numbers that can only be divided by 1 and itself). There are admittedly a number of different ways each number can be factored; however, for larger numbers, it may. be easiest to go with a simple approach at first. We can see that 400, 288, and 504 are all even numbers, which means that they can all be divided by 2. We will continue this pattern of dividing by 2 until we can recognize a number that can be divided more easily using other numbers. Starting with 400: If we divide 400 by 2, we end up with 2 and 200. (Prime numbers: 2) 200 can be divided by 2 again to yield 2 and 100. (Prime numbers: 2, 2) 100 can be divided by 2 again to yield 2 and 50. (Prime numbers: 2, 2, 2) 50 can be divided by 2 again to yield 2 and 25. (Prime numbers: 2, 2, 2, 2) 25 can then be divided by 5 to yield 5 and 5. (Prime numbers: 2, 2, 2, 2, 5, 5) Thus, we have found that the prime factors of 400 are 2, 2, 2, 2, 5, 5. We can check if we did our factorization correctly by multiplying all the prime factors together. If factored correctly, the new value should equal our original value of 400. This same process can be applied to the other two numbers. 288 can be divided by 2 to yield 144 and 2. (Prime numbers: 2) 144 can be divided by 2 to yield 72 and 2. (Prime numbers: 2, 2) 72 can be divided by 2 to yield 36 and 2. (Prime numbers: 2, 2, 2) 36 can be divided by 6 to yield 6 and 6. (Prime numbers: 2, 2, 2) Each 6 can be divided by 2 to yield 2 and 3. (Prime numbers: 2, 2, 2, 2, 2, 3, 3) Thus, we have found that the prime factors of 288 are 2, 2, 2, 2, 2, 3, 3. Finally, 504 can be divided by 2 to yield 252 and 2. (Prime numbers: 2) 252 can be divided by 2 to yield 126 and 2. (Prime numbers: 2, 2) 126 can be divided by 2 to yield 63 and 2. (Prime numbers: 2, 2, 2) 63 can be divided by 7 to yield 9 and 7. (Prime numbers: 2, 2, 2, 7) 9 can be divided by 3 to yield 3 and 3. (Prime numbers: 2, 2, 2, 3, 3, 7). Thus, we have found that the prime factors of 504 are 2, 2, 2, 3, 3, 7. The final step is to determine what prime factors are common across all three numbers. A value like 3 is not considered because although it is present as a prime factor in 504 and 288, it is not present in 400. We can see that 400, 288, and 504 each share three distinct 2s across their prime factors. These shared prime factors are then multiplied by one another to give the greatest common factor. 2 x 2 x 2 = 8. Thus, 8 is the greatest common factor of 400, 288, and 504.
Subject: Basic Chemistry
Which of the following has a larger radius: Cl- or Ar?
What is important to recognize is that Cl- and Ar are isoelectronic - in other words, they share the same electronic configuration. This is because we are not comparing two atomic radii but rather the radii of a chloride ion (which has an additional electron added to its ground state electronic configuration) and an argon atom. The electronic configuration for both the chloride ion and the argon atom is 1s2 2s2 2p6 3s2 3p6 aka [Ne] 3s2 3p6. Thus, we know that Cl- and Ar are identical in the number of electrons. What differentiates the two is the mass number - the number of protons and neutrons. Neutrons do not have any significant effect on the radius so that value can be disregarded. Based on the periodic table, we know that a chloride ion has 17 protons while an argon atom as 18. Argon has an additional proton that contributes more strongly to the electrostatic force between its positively charged nucleus and negatively charged valence electrons (because opposites attract). Thus, the stronger force in the argon atom ultimately pulls in the valence electrons more strongly than the force in the chloride ion, making the radius of Cl- larger than the radius of Ar.
Do arteries always carry oxygenated blood?
While it may be tempting to think that the defining characteristic of an artery is that it carries oxygenated blood, this is not always the case. An artery is actually defined as a blood vessel that serves to carry blood away from the heart. There are two types of arteries that carry deoxygenated blood: the pulmonary arteries and the umbilical arteries. In both instances, the arteries are directing blood away from the heart so the gas exchange can occur; the pulmonary arteries are bringing deoxygenated blood away from the heart and towards the lungs while the umbilical arteries bring deoxygenated blood from the baby to the placenta (it is important to note that in this case, the arteries are moving blood away from the baby's heart, not the mother's).
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