Factoring and Multiples

There aren't any whole numbers that satisfy these conditions. The only numbers that multiply to 23 are 23 and 1.

Oh, dude, the greater common factor of 72 and 180 is 36. It's like when you're trying to find the biggest number that can divide both 72 and 180 without leaving any remainder. So, yeah, 36 is the winner here. Cool, right?

2 times 34 =68

Oh, isn't that just lovely? Let's take a moment to appreciate the beauty of numbers working together. The common factors of 54 and 66 are 1, 2, 3, 6 - just like little friends coming together to create harmony on our canvas. Remember, every number has its place and purpose, just like every brushstroke adds to the masterpiece of life.

To express 16 as a product of prime factors, we first note that 16 is an even number, so we can divide it by 2. 16 divided by 2 equals 8. 8 is also divisible by 2, so we divide it by 2 again to get 4. Finally, 4 is divisible by 2, giving us 2 x 2 x 2 x 2, or 2^4. Therefore, 16 can be expressed as 2^4.

To find the factor tree for 188, we start by identifying two factors of 188 that multiply to give 188. One possible pair is 4 and 47. Then, we continue factoring these numbers until we reach their prime factors. The factor tree for 188 would be:

188 /
4 47 /
2 2 47

Therefore, the prime factorization of 188 is 2 x 2 x 47.

1 and 4

1 x 360000, 2 x 180000, 3 x 120000, 4 x 90000, 5 x 72000, 6 x 60000, 8 x 45000, 9 x 40000, 10 x 36000, 12 x 30000, 15 x 24000, 16 x 22500, 18 x 20000, 20 x 18000, 24 x 15000, 25 x 14400, 30 x 12000, 32 x 11250, 36 x 10000, 40 x 9000, 45 x 8000, 48 x 7500, 50 x 7200, 60 x 6000, 64 x 5625, 72 x 5000, 75 x 4800, 80 x 4500, 90 x 4000, 96 x 3750, 100 x 3600, 120 x 3000, 125 x 2880, 144 x 2500, 150 x 2400, 160 x 2250, 180 x 2000, 192 x 1875, 200 x 1800, 225 x 1600, 240 x 1500, 250 x 1440, 288 x 1250, 300 x 1200, 320 x 1125, 360 x 1000, 375 x 960, 400 x 900, 450 x 800, 480 x 750, 500 x 720, 576 x 625, 600 x 600 = 360,000

Oh, dude, the highest common factor of 756? That's like the biggest number that can divide 756 without leaving a remainder. So, the highest common factor of 756 is 756 itself. It's like the king of factors for that number.

Oh, dude, like, the least common multiple (LCM) of 27, 84, and 90 is 756. It's basically the smallest number that all three of those numbers can divide into evenly. So, if you're ever at a party and someone asks you for the LCM of 27, 84, and 90, you can totally impress them with that number.

To find the greatest common factor (GCF) of 24, 32, and 48, we need to determine the largest number that divides evenly into all three numbers. First, we find the factors of each number: 24 (1, 2, 3, 4, 6, 8, 12, 24), 32 (1, 2, 4, 8, 16, 32), and 48 (1, 2, 3, 4, 6, 8, 12, 16, 24, 48). The GCF of 24, 32, and 48 is 8, as it is the largest number that appears in the factor lists of all three numbers.

To express 650 as the product of prime factors, we first divide it by the smallest prime number, which is 2. This gives us 325. Then, we divide 325 by 5, another prime number, to get 65. Continuing this process, we divide 65 by 5 to get 13, which is a prime number. Therefore, the prime factorization of 650 is 2 x 5 x 5 x 13.

Since 27y is a factor of 54y3, it is automatically the GCF.

The Highest Common Factor (HCF) of 12 and 90 is 6. To find the HCF, you can list the factors of both numbers and identify the largest number that is common to both lists. The factors of 12 are 1, 2, 3, 4, 6, and 12, while the factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90. The largest number that appears in both lists is 6, making it the HCF.

6 x (500 over 3) is equal to 1000

Well, darling, the quotient of 16 divided by 8 is 2. It's as simple as that. Math doesn't have to be complicated, sugar. Just divide those numbers and you've got your answer.

the first 6 multiples of 12 are 12,24,36,48,60, and 72.

The GCF is 14.

Oh, dude, you're hitting me with the math questions. Alright, so the factors of 448 are 1, 2, 4, 7, 8, 14, 16, 28, 56, 112, 224, and 448. Like, it's basically all the numbers that you can multiply together to get 448. So, yeah, there you go, math wizard.

Factors refer to integers, not mixed numbers.

Oh, dude, the Highest Common Factor of 80? That's just the biggest number that can divide evenly into 80. So, like, the HCF of 80 is 80 itself because it's the highest number that can go into 80 without leaving a remainder. Easy peasy, right?

Oh, dude, you're hitting me with the math questions? Alright, so the odd composite factors of 60 are the numbers that can divide into 60, besides 1 and 60. So, the odd composite factors of 60 are 3, 5, 15. There you go, a little math mixed with some sarcasm for ya!

The prime factorization of 44 using exponents is 2^2 x 11. This means that 44 can be expressed as the product of 2 raised to the power of 2 (2^2) and 11. In other words, 44 = 2 x 2 x 11. This representation helps break down the number into its prime factors for easier analysis and computation.

Sure thing, honey. To write 128 in expanded notation using exponents, you'd express it as 1 x 10^2 + 2 x 10^1 + 8 x 10^0. So, it would be 1 x 100 + 2 x 10 + 8 x 1. Easy peasy lemon squeezy.

The Greatest Common Factor (GCF) of 90 and 180 is 90. To find the GCF, you can list the factors of each number and determine the largest number that divides both numbers evenly. The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90. The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180. The largest number that appears in both lists is 90, making it the Greatest Common Factor.