Factoring and Multiples

The greatest common factor (GCF) is often also called the greatest common divisor (GCD) or highest common factor (HCF). Keep in mind that these different terms all refer to the same thing: the largest integer which evenly divides two or more numbers.

The greatest common factor of 13 and 52 is 13

36 x 1

18 x 2

12 x 3

9 x 4

6 x 6

The least common multiple (LCM) is often also called the lowest common multiple or smallest common multiple. Keep in mind that these different terms all refer to the same thing: the smallest positive integer which is a multiple of two or more numbers.

The least common multiple of 5 and 234 is 1170.

The least common multiple (LCM) of 5 and 7 is 35, not the least common denominator (LCD). The LCD is used in adding or subtracting fractions and is the least common multiple of the denominators. In this case, since 5 and 7 are prime numbers and have no common factors, the LCD is simply the product of the two denominators, which is 5 * 7 = 35.

To find what equals 122 when multiplied, we need to factorize 122 into its prime factors. 122 can be expressed as 2 x 61. Therefore, 2 multiplied by 61 equals 122.

Oh, dude, the greatest common factor of 77, 132, and 143 is 11. It's like the cool kid that all these numbers have in common. So, if you're throwing a math party with these numbers, 11 is the VIP guest that gets in everywhere.

Well, isn't that a happy little question! To find the Least Common Multiple (LCM) of 24, 72, and 96, we can start by listing the prime factors of each number. Then, we take the highest power of each prime factor that appears in any of the numbers. By doing this, we find the LCM, which is 288. Just like painting a beautiful landscape, finding the LCM is all about taking your time and following a methodical approach.

4x^(2) - 8x

'4' is common to both '4' & '8' . So tak outr '4'.

Hence

4(x^(2) - 2x)

Inside the brackets 'x' is common to both 'x^(2) & '2x'. So take out 'x'.

Hence

4x(x - 2)

Done , fully factored.

7 x 2 =14

7 x 3 = 21

7 x 5 = 35

7 x 10 = 7 x 2 x 5 = 70

'7' appears in each multiple .sp '7' is thre HCF.

4 goes into 64 exactly 16 times

The greatest common factor (GCF) is often also called the greatest common divisor (GCD) or highest common factor (HCF). Keep in mind that these different terms all refer to the same thing: the largest integer which evenly divides two or more numbers.

The greatest common factor of 132 and 242 is 22

Oh, what a lovely puzzle to solve! Let's paint a happy little picture here. If we have four odd numbers that are multiples of 5 and their sum is 80, we can see that the numbers are 5, 15, 25, and 35. Each number is odd, a multiple of 5, and when you add them together, you get a beautiful total of 80. Happy painting!

Well, honey, the number you're looking for is 150. It's greater than 100, and it's in both the three times tables (3 x 50) and the five times tables (5 x 30). So there you have it, no need to overcomplicate things, darling.

15

30 = 2 x 3 x 5

75 = 3 x 5^2

120 = 2^3 x 3 x 5

gcf = 3 x 5 = 15

The highest common factor (HCF) of two numbers is the largest number that divides both of them without leaving a remainder. To find the HCF of 150 and 75, we can use the method of prime factorization. The prime factors of 150 are 2 x 3 x 5 x 5, and the prime factors of 75 are 3 x 5 x 5. By comparing the common prime factors, we see that the HCF of 150 and 75 is 3 x 5, which equals 15.

The GCF of 91, 156, and 169 is 13.
It is: 13

The number 300 can be divided by 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, and 300. These numbers are factors of 300 because they divide evenly into 300 without leaving a remainder.

The prime factors of 180a2 are 2, 2, 3, 3, 5, a, and a.

The prime factors of 210a are 2, 3, 5, 7, and a.

The prime factors in common are 2, 3, 5, and a, so the greatest common factor is 2 x 3 x 5 x a = 30a. If a is divisible by 7, there would be two factors of 7 in a2, so the extra 7 would be another factor in common with 210a, in which case the greatest common factor would be 7 x 30a = 210a

2 x 3 x 5 is the prime factorization of 30.

To find the greatest common factor (GCF) of 18, 54, and 90, we first need to find the prime factorization of each number. The prime factorization of 18 is 2 * 3^2, the prime factorization of 54 is 2 * 3^3, and the prime factorization of 90 is 2 * 3^2 * 5. To find the GCF, we identify the common prime factors among the numbers, which are 2 and 3^2. Therefore, the GCF of 18, 54, and 90 is 2 * 3^2, which equals 18.

Oh, what a happy little question! To find the prime factorization of 96, we break it down into its prime factors: 2 x 2 x 2 x 2 x 2 x 3. In index form, this would be written as 2^5 x 3. Keep on painting those mathematical landscapes, my friend!

Oh, dude, it's like super easy. So, you take 8204 and break it down into its place values. It's 8000 + 200 + 4. Then you write each of those numbers with exponents: 8 x 10^3 + 2 x 10^2 + 4. Boom, that's how you do it.

I suppose you could use -42 twice.

-63 and -21

Yes, there is a greatest common factor (GCF) of 15, 72, and 108. To find the GCF, you need to factor each number into its prime factors. The prime factorization of 15 is 3 x 5, 72 is 2^3 x 3^2, and 108 is 2^2 x 3^3. The GCF is the product of the common prime factors raised to the lowest power, which in this case is 3 x 2^2 = 12.

Oh, what a happy little question! To find a number with 8 factors, we look for numbers that can be expressed as the product of two prime numbers. The smallest number less than 50 with 8 factors is 30, which can be written as 2 x 3 x 5. Keep exploring and painting with numbers, there are so many beautiful patterns to discover!