Factoring and Multiples

To find a number between 49 and 95 that is a multiple of 3, 9, and 12, we need to find the least common multiple (LCM) of these three numbers. The LCM of 3, 9, and 12 is 36. To find a number between 49 and 95 that is a multiple of 36, we can start with 72 (which is 2 times 36) as the smallest number in that range. Therefore, the number between 49 and 95 that is a multiple of 3, 9, and 12 is 72.

To find the least common multiple (LCM) of 45, 54, and 72, we first need to find the prime factorization of each number. The prime factorization of 45 is 3^2 * 5, 54 is 2 * 3^3, and 72 is 2^3 * 3^2. Then, we take the highest power of each prime factor that appears in any of the numbers: 2^3 * 3^3 * 5 = 540. Therefore, the LCM of 45, 54, and 72 is 540.

Oh, dude, the greatest common factor of 42, 56, and 63 is 7. It's like the cool kid at the math party that all three numbers can hang out with without any drama. So yeah, 7 is the GCF, but don't worry too much about it, math can be chill too, you know?

Oh, isn't that just a happy little math problem? To find the Least Common Multiple (LCM) of 96, 144, and 240, we can start by listing the prime factors of each number. Then, we can take the highest power of each prime factor that appears in any of the numbers. Combine these powers together, and you'll have your LCM, creating a beautiful harmony of numbers just like a painting coming together on canvas.

200 = 2 x 2 x 2 x 5 x 5 or 23 x 52

Oh, isn't that a happy little number! Let's break it down gently. To express 344 as a product of prime factors, we can start by dividing it by the smallest prime number, which is 2. This gives us 2 x 2 x 2 x 43, showing that 344 can be written as 2^3 x 43. And just like that, we've created a beautiful prime factorization of 344.

To find the least common multiple (LCM) of two numbers, you first need to find the prime factorization of each number. The prime factorization of 275 is 5 x 5 x 11, and the prime factorization of 605 is 5 x 11 x 11. To find the LCM, you take the highest power of each prime factor that appears in either factorization: 5^2 x 11^2 = 3025. Therefore, the LCM of 275 and 605 is 3025.

To find the least common multiple (LCM) of 17, 51, and 85, we first need to find the prime factorization of each number. The prime factorization of 17 is 17, the prime factorization of 51 is 3 x 17, and the prime factorization of 85 is 5 x 17. The LCM is the product of all the prime factors, each taken to the highest power it occurs in any of the numbers. Therefore, the LCM of 17, 51, and 85 is 5 x 3 x 17 = 255.

The greatest common factor (GCF) of 2mn and 4m^2n^2 can be found by breaking down each term into its prime factors. For 2mn, the prime factors are 2, m, and n. For 4m^2n^2, the prime factors are 2, 2, m, m, n, and n. The GCF is the product of the common prime factors raised to the lowest power they appear in both terms, which in this case is 2mn. Therefore, the GCF of 2mn and 4m^2n^2 is 2mn.

Two pairs of numbers with 105 as their least common multiple are (15, 105) and (21, 105). This means that both pairs of numbers are multiples of 105 and their only common multiple is 105. The least common multiple is the smallest number that both numbers can divide evenly into.

The GCF is 44.

The GCF is 4.

Well, honey, a factor of 14 that isn't a multiple of 7 is 2. You see, a factor of a number divides into it evenly, while a multiple is the result of multiplying a number by an integer. So, in this case, 2 fits the bill perfectly. Hope that clears things up for ya, sugar!

The Greatest Common Factor of 14, 43, 49 is 1.

360 = 1 x 360, 2 x 180, 3 x 120, 4 x 90, 5 x 72, 6 x 60, 8 x 45, 9 x 40, 10 x 36, 12 x 30, 15 x 24, 18 x 20, 20 x 18, 24 x 15, 30 x 12, 36 x 10, 40 x 9, 45 x 8, 60 x 6, 72 x 5, 90 x 4, 120 x 3, 180 x 2, 360 x 1.

8 goes into 9, zero times with a remainder of 9. In division, the number being divided (9) is called the dividend, the number doing the dividing (8) is called the divisor, the result (0) is called the quotient, and the remaining amount (9) is called the remainder.

The common multiples of 3 and 8 are 24, 48, 72, 96, 120, and so on. The LCM (least common multiple) of 3 and 8 is 24.

To solve the equation -4.8 + 6.4 - 8.48, you first add the -4.8 and 6.4 together to get 1.6. Then, you subtract 8.48 from 1.6 to get -6.88. Therefore, the solution to the equation is -6.88.

Oh, dude, the HCF of 6, 12, and 24 is 6. It's like the cool kid that all three numbers can hang out with without any drama. So yeah, 6 is the highest common factor they all have in common. Cool, right?

Oh, dude, it's like simple math. If you have a number and you wanna find out what times what equals 140, you just gotta think about it for a sec. So, like, 10 times 14 equals 140. Easy peasy, lemon squeezy.

The fact family of 3, 9, and 27 involves multiplication and division relationships. In this case, the numbers 3, 9, and 27 are related as follows: 3 x 9 = 27, 9 x 3 = 27, 27 ÷ 9 = 3, and 27 ÷ 3 = 9. These equations demonstrate the fact family connections between the numbers 3, 9, and 27 through multiplication and division operations.

The GCF of 32 and 48 is 16.

32 + 48 = (2 x 16) + (3 x 16) = 5 x 16 = 80

The positive integer factors of 30 are:

1 2 3 5 6 10 15 30

The odd factors are therefore 1, 3, 5, 15

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