Factoring and Multiples

Oh, dude, the pairs of integers A and B that have a greatest common divisor of 18 and a least common multiple of 540 are like (18, 540) and (-18, -540). It's like finding a needle in a haystack, but hey, that's math for you. So yeah, those pairs fit the bill.

9 and 10 share no common factors aside from 1.

The Highest Common Factor (HCF) of 189 and 84 is the largest positive integer that divides both numbers without leaving a remainder. To find the HCF, you can use the Euclidean algorithm, which involves repeatedly dividing the larger number by the smaller number and using the remainder as the new divisor until the remainder is zero. In this case, the HCF of 189 and 84 is 21.

Shell program to find LCM and hcf of two no.s

tput clear

echo "Enter first no"

read a

echo "Enter 2nd no"

read b

p= 'expr $a \* $b'

while [$b -ne 0]

do

r= 'expr $a % $b'

a=$b

b=$r

done

LCM = 'expr $p / $a'

echo "LCM = $LCM"

echo "Hcf = $a"

Ah, what a happy little question we have here! The common factor of 16 and 20 is 4. You see, a common factor is a number that can divide into both 16 and 20 without leaving a remainder. Just like how we blend colors on our palette, finding common factors is a gentle way of seeing the connections between numbers.

Well, honey, the number 12 takes the crown in this factor frenzy. It has a whopping 6 factors: 1, 2, 3, 4, 6, and 12. So, if you're looking for the popular kid on the block in terms of factors, 12 is your go-to choice.

Well, honey, to find the number of 4-digit multiples of 9, you just need to divide the largest 4-digit multiple of 9 (9999) by 9 and subtract the smallest 4-digit multiple of 9 (1008) divided by 9. So, 9999 ÷ 9 - 1008 ÷ 9 = 1111 - 112 = 999. That's right, there are 999 4-digit numbers that are multiples of 9.

To find the least common multiple (LCM) of 16, 18, and 20, we first need to find the prime factorization of each number. The prime factorization of 16 is 2^4, 18 is 2 * 3^2, and 20 is 2^2 * 5. To find the LCM, we take the highest power of each prime factor that appears in any of the numbers: 2^4 * 3^2 * 5 = 720. Therefore, the least common multiple of 16, 18, and 20 is 720.

Well, darling, the prime factors of 240 are 2, 2, 2, 2, 3, and 5. Now, if you add those bad boys up, you get 16. So, the sum of the prime factors of 240 is 16. Hope that tickles your fancy!

Oh, what a happy little math question we have here! When we see 26(x3), we can simply multiply 26 by 3 to get 78. So, 26 multiplied by 3 is 78. Great job exploring the world of numbers!

Well, well, well, look who's trying to factor a quadratic equation! To factor 2x^2 + 11x + 14, you need to find two numbers that multiply to 28 (2*14) and add up to 11. Those numbers are 2 and 14. So, the factored form is (2x + 7)(x + 2). Voila!

The longest factor string for 42 is when we break down 42 into its prime factors. 42 can be expressed as 2 x 3 x 7. This is the longest factor string because these are the prime numbers that, when multiplied together, result in 42.

3 (if "between 3-200" includes 3), 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99, 102, 105, 108, 111, 114, 117, 120, 123, 126, 129, 132, 135, 138, 141, 144, 147, 150, 153, 156, 159, 162, 165, 168, 171, 174, 177, 180, 183, 186, 189, 192, 195, and 198 are all multiples of 3 between 3 and 200.

The greatest common factor (GCF) of 48 and 60 is the largest number that divides both 48 and 60 without leaving a remainder. To find the GCF, you can list the factors of each number and identify the largest factor they have in common. The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48, while the factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. The largest factor that both 48 and 60 share is 12, making the GCF of 48 and 60 equal to 12.

To find the common monomial factor of a set of monomials, first identify the variables and their corresponding exponents in each monomial. Next, determine the smallest exponent for each variable that appears in all the monomials. Finally, combine the variables with their corresponding smallest exponents to form the common monomial factor. This factor will be the largest monomial that can be factored out from each original monomial.

Numbers that can be divided into 3 and 4 without a remainder are multiples of both 3 and 4, which are also known as common multiples. The least common multiple of 3 and 4 is 12, so any number that is a multiple of 12 can be divided by both 3 and 4 without a remainder. This includes numbers like 12, 24, 36, 48, and so on.

Well, well, well, look who's trying to flex their math muscles! The least common multiple of 100 and 125 is 500. You're welcome for the knowledge drop, honey.

The greatest common factor of 133 and 203 is 7

Oh, what a happy little question! To find the greatest common factor of 280 and 332, we can first list the factors of each number. The factors of 280 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, and 280, while the factors of 332 are 1, 2, 4, 83, 166, and 332. The greatest common factor is the largest number that appears in both lists, which in this case is 4.

The greatest common factor (GCF) of 16 and 81 is 1. This is because the factors of 16 are 1, 2, 4, 8, and 16, while the factors of 81 are 1, 3, 9, 27, and 81. The only factor that they have in common is 1, making it the greatest common factor.

Well, isn't that a happy little question! The greatest common factor of 38 and 48 is 2. You see, the greatest common factor is the largest number that divides evenly into both 38 and 48, and in this case, 2 is that special number. Just like painting a beautiful landscape, finding the greatest common factor is all about looking for the common elements that bring everything together in harmony.

To determine if 3 is a factor of 261, we need to check if 261 is divisible by 3 without any remainder. We can do this by dividing 261 by 3. When we divide 261 by 3, we get 87 with no remainder. Therefore, 3 is a factor of 261 because it divides evenly into 261.

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The Greatest Common Factor (GCF) of 36, 64, and 72 is 4, as it is the largest number that divides evenly into all three numbers. The Least Common Multiple (LCM) of 36, 64, and 72 is 576, as it is the smallest multiple that is divisible by all three numbers. The GCF is found by identifying the common factors of the numbers and selecting the largest one, while the LCM is determined by multiplying the prime factors of the numbers.