Factoring and Multiples

As a product of its prime factors: 2*2*2*3*3*5 = 360

To find the greatest square factor of 675, we need to break down 675 into its prime factors: 3 x 3 x 3 x 5 x 5. To identify the square factors, we look for pairs of the same prime factors. In this case, we have two 3's and two 5's. Multiplying these pairs together gives us the greatest square factor of 675, which is 3 x 3 x 5 x 5 = 225.

Well, honey, the factors of 1234567890 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90, 13717421, 27434842, 41152263, 68587105, 823044126, and 1234567890. So, there you have it, all the factors of that big ol' number. Hope that helps, sugar!

Well, isn't that a happy little math problem! Let's see, the two numbers that multiply to 28 and add up to 16 are 4 and 7. Just like painting a beautiful landscape, sometimes all it takes is a little patience and a gentle touch to find the right solution. Happy problem-solving, my friend!

The greatest common factor (GCF) of 4a and 10a is 2a. To find the GCF, we need to identify the largest factor that both 4a and 10a have in common. In this case, both 4a and 10a can be divided by 2 and a, making 2a the greatest common factor.

Oh, dude, let me break it down for you. The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42. For 56, you've got 1, 2, 4, 7, 8, 14, 28, and 56. And lastly, 140 rolls in with 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, and 140. Like, that's the whole squad right there.

To find two numbers that multiply to 1260, we can start by finding the prime factorization of 1260, which is 2^2 * 3^2 * 5 * 7. From this prime factorization, we can see that the two numbers that multiply to 1260 are 2 * 2 * 3 * 3 * 5 * 7, which simplifies to 60 and 21. Therefore, 60 and 21 are the two numbers that multiply to 1260.

Oh, dude, the greatest common factor of 3 and 64 is 1. Like, they don't have any common factors other than 1 because 3 is a prime number and 64 is, well, 64. So, yeah, that's the deal with that.

A factor is a number that divides another number without leaving a remainder. In the equation 7x7=49, the number 7 is a factor because it divides evenly into 49, resulting in a whole number quotient of 7. Therefore, 7 is a factor of 49 in this case.

Well, darling, the Highest Common Factor of 54 and 135 is 27. It's like finding the biggest diva that both numbers can bow down to without any drama. So, there you have it, the HCF is 27, case closed.

Oh, isn't that a happy little number! The factors of 100,000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000, 2000, 5000, 10000, and 20000. The prime factors are 2 and 5, repeated multiple times. Just imagine those factors and prime factors dancing together in perfect harmony on your canvas of mathematics!

Yes, 54 is a multiple of 3. A multiple of a number is obtained by multiplying that number by an integer. In this case, 54 divided by 3 equals 18, which is an integer. Therefore, 54 is a multiple of 3.

Oh, what a happy little question! To find a number divisible by 2, 3, 5, 6, and 10, we need to look for the least common multiple of these numbers. The smallest 3-digit number that fits the bill is 120. Just like painting a beautiful landscape, finding the right number takes patience and a gentle touch.

The greatest common factor (GCF) of two numbers is the largest number that divides both numbers without leaving a remainder. In this case, the numbers 74 and 37 are both prime numbers, meaning they are only divisible by 1 and themselves. Therefore, the GCF of 74 and 37 is 1.

Oh honey, the greatest common factor of 15, 36, and 70 is 1. Those numbers don't have any common factors other than 1, so you're out of luck if you were hoping for something more exciting. But hey, at least now you know!

Oh, dude, the smallest number with 2, 5, and 7 as prime factors is 70. It's like the VIP of numbers, with all those cool prime factors hanging out together. So, yeah, 70 is the magic number you're looking for.

The greatest common factor (GCF) of two numbers is the largest number that divides both numbers evenly. To find the GCF of 36 and 162, you need to determine the common factors of both numbers. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36, while the factors of 162 are 1, 2, 3, 6, 9, 18, 27, 54, and 162. The largest number that appears in both lists is 18, so the GCF of 36 and 162 is 18.

Well, honey, the highest common factor (HCF) of 60 and 63 is 3. You see, 60 can be broken down into 2 x 2 x 3 x 5, while 63 can be broken down into 3 x 3 x 7. The highest common factor is just the highest number that appears in both factorizations, which in this case is 3.

To find the least common multiple (LCM) of 3, 8, and 12, we first need to find the prime factorization of each number. The prime factorization of 3 is 3, 8 is 2 x 2 x 2, and 12 is 2 x 2 x 3. To calculate the LCM, we take the highest power of each prime factor that appears in any of the numbers: 2^3 x 3 = 24. Therefore, the least common multiple of 3, 8, and 12 is 24.

The algebra teacher's advice on successful dieting likely involved the concept of balancing input and output. In algebra, this can be represented by equations where the intake of calories is equal to or less than the calories burned through physical activity. This advice emphasizes the importance of calorie management and understanding the mathematical relationship between food consumption and energy expenditure to achieve weight loss or maintenance.

If 3 is not a common factor of a pair of numbers, then other numbers that cannot be common factors are any multiples of 3, such as 6, 9, 12, and so on. This is because if a number is a multiple of 3, it will also be divisible by 3, making it a common factor. Additionally, any prime numbers that are not factors of 3, such as 2, 5, 7, 11, and so on, cannot be common factors either.

Oh, dude, you're hitting me with some math vibes. So, the numbers that multiply to equal 280 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, and of course, 280. Like, that's the whole squad right there.

Yes, 78 is a composite number. A composite number is a positive integer that has more than two distinct positive divisors. In the case of 78, it has divisors other than 1 and itself, such as 2, 3, 6, 13, 26, and 39.

Alright, buckle up, buttercup. The highest common factor of 91, 143, and 156 is 13. That's right, 13 is the biggest number that can divide evenly into all three of those numbers. So, there you have it, 13 is the boss in this HCF showdown.

Well, honey, the highest common factor (HCF) of 39, 143, and 169 is 13. There you have it, no need for any fancy footwork or beating around the bush. Just straight to the point like a boss.