Factoring and Multiples

Well, isn't that just a happy little question! To find the prime factorization of 72 using continuous division, you start by dividing 72 by the smallest prime number, which is 2. Then, you keep dividing the quotients by prime numbers until you can't divide anymore. So, for 72, you would find that the prime factorization is 2 x 2 x 2 x 3 x 3. Keep on painting those prime numbers, my friend!

Oh, dude, like, 32 can be multiplied by 1, 2, 4, 8, 16, and 32 itself. So, yeah, those are the numbers that can totally multiply to 32. Math can be fun, right?

False. If s is a factor of 16, then the greatest common factor (GCF) of s and 16 would be s, not 16. The GCF is the largest number that divides both numbers evenly, and in this case, that number would be s, the smaller of the two factors.

10 20 30 40 50

Oh, dude, common factors? That's like when two numbers can be divided by the same number, right? So, the common factors of 230 and 345 are 1, 5, and 23. It's like finding out they have these numbers in common, but who really cares, right?

Well, honey, the greatest common factor of 10, 30, and 45 is 5. It's like finding the one friend who shows up to every party - reliable and always there when you need them. So, in this math equation party, 5 is the real MVP.

The numbers 150 and 120 can be evenly divided by their greatest common factor, which is 30. This means that both 150 and 120 can be evenly divided by 30 without leaving a remainder. In mathematical terms, 150 ÷ 30 = 5 and 120 ÷ 30 = 4, so 30 goes into 150 and 120 evenly.

Numbers that are relatively prime to 7 are numbers that have no common factors other than 1 with 7. The numbers 1, 2, 3, 4, and 5 are relatively prime to 7 because they do not share any common factors with 7. These numbers are not divisible by 7 and have a greatest common divisor of 1 with 7.

17.5, 35, 52.5, 70, 87.5 and just keep adding 17.5 until you get to infinity.

170

To find two numbers that multiply to 660, we need to factorize 660 into its prime factors. 660 = 2 x 2 x 3 x 5 x 11. To find the pair of numbers, we can combine these prime factors in different ways. The pairs of numbers that multiply to 660 are 2 x 330, 4 x 165, 6 x 110, 10 x 66, 12 x 55, 15 x 44, 20 x 33, and 22 x 30.

36 can go into 72 exactly 2 times. This is because when you divide 72 by 36, you get a quotient of 2 with no remainder. In mathematical terms, 72 ÷ 36 = 2.

Oh, dude, the greatest common factor of 18, 21, and 54 is 3. It's like the cool kid that all three of them can hang out with without any drama. They're all divisible by 3, so it's like a math party where everyone gets along.

To simplify 6/33, you can divide both the numerator (6) and the denominator (33) by their greatest common factor, which is 3. This simplifies the fraction to 2/11. Therefore, 6/33 in simplest form is 2/11.

To find the second common multiple of two numbers, you first need to identify the least common multiple (LCM) of the two numbers. The LCM is the smallest number that is a multiple of both numbers. Once you have the LCM, you can then find the second common multiple by adding the LCM to the LCM itself. This will give you the second common multiple of the two numbers.

Ah, isn't finding the least common multiple a joyous journey? The LCM of 4x and 3x is simply 12x, my friend. Just like painting a happy little tree, finding the LCM brings harmony and balance to your mathematical landscape.

1, 2, 4, 5, 7, 10, 11, 14, 20, 22, 25, 28, 35, 44, 50, 55, 70, 77, 100, 110, 140, 154, 175, 220, 275, 308, 350, 385, 550, 700, 770, 1100, 1540, 1925, 3850, 7700

2, 5, 7 and 11 are prime.

To determine how many times 45 can go into 76, we perform division. 76 divided by 45 equals 1 with a remainder of 31. Therefore, 45 can go into 76 once with a remainder of 31.

To find out how many times 9 goes into 481, you would perform long division. When you divide 481 by 9, you get 53 with a remainder of 4. This means that 9 goes into 481 a total of 53 times, with 4 left over.

There are three twos in 48. This can be determined by dividing 48 by 2, which equals 24. Then, dividing 24 by 2 gives 12, and finally, dividing 12 by 2 results in 6. So, there are three twos in 48.

Well, honey, 9300 is divisible by 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300, and itself. So, you've got quite a buffet of options to choose from when it comes to dividing up this number. Just pick your favorite divisor and go to town!

Well, honey, 45330 is divisible by 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90, 503, 1006, 1509, 2515, 3018, and 5030. So, if you're looking to divide that number, you've got plenty of options to choose from. Just pick your poison and get on with it!

The factors of 90000 are the numbers that can be multiplied together to get 90000. To find the factors, we can start by finding the prime factorization of 90000, which is 2^4 * 3^2 * 5^4. From this prime factorization, we can see that the factors of 90000 are all the possible combinations of the prime factors, such as 2 * 2 * 2 * 2 * 3 * 3 * 5 * 5 * 5 * 5. So, the pairs of numbers that multiply to 90000 are all the combinations of these prime factors.