Factoring and Multiples

Ah, finding the greatest common factor is like finding a happy little tree in a forest. For 36 and 81, we look for the largest number that can divide evenly into both. The greatest common factor for 36 and 81 is 9, like a gentle breeze on a sunny day.

A factor is a divisor - a number that will evenly divide into another number. The greatest common factor of two or more numbers is the largest factor that both numbers have in common.

One way to determine the common factors and greatest common factor is to find all the factors of the numbers and compare them.

The factors of 125 are 1, 5, 25, and 125.

The factors of 175 are 1, 5, 7, 25, 35, and 175.

The common factors are 1, 5, and 25. Therefore, the greatest common factor is 25.

Well, darling, the greatest common factor of 6 and 32 is 2. You see, 2 is the largest number that can divide both 6 and 32 without leaving a remainder. So, there you have it - 2 is the winner in this mathematical showdown.

64

Well, honey, to make a factor tree for 69, you'll need to break it down into its prime factors. 69 can be broken down into 3 and 23, which are both prime numbers. So, the factor tree for 69 would have 3 and 23 as its branches. Hope that clears things up for ya!

Example: 30 and 42

Factor them.

2 x 3 x 5 = 30

2 x 3 x 7 = 42

Select the common factors.

2 x 3 = 6, the GCF

Combine the factors, eliminating duplicates.

2 x 3 x 5 x 7 = 210, the LCM

Check it.

30 x 42 = 1260

210 x 6 = 1260

It checks.

1/5 of 25 is equal to 25 divided by 5, which equals 5. This means that if you take one-fifth of the number 25, you are left with the value of 5.

To find two numbers that multiply to 644, we can factorize 644 into its prime factors: 2 x 2 x 7 x 23. From this, we can see that 2 x 322 equals 644, so the two numbers are 2 and 322.

1, 3 and 9

The ratio of 24 to 48 can be simplified by dividing both numbers by their greatest common factor, which is 24. So, 24 ÷ 24 = 1 and 48 ÷ 24 = 2. Therefore, the simplified ratio is 1:2. This means that for every 1 unit of 24, there are 2 units of 48.

To find the greatest common factor (GCF) of 324, 180, and 120 using prime factorization, we first break down each number into its prime factors.

324 = 2^2 * 3^4 180 = 2^2 * 3^2 * 5 120 = 2^3 * 3 * 5

Next, we identify the common prime factors among the numbers: 2^2, 3, and 5.

Multiplying these common prime factors together, we get the GCF: 2^2 * 3 * 5 = 60.

Therefore, the GCF of 324, 180, and 120 using prime factorization is 60.

11 times

Oh, dude, you want me to do math? Fine, fine. So, like, numbers divisible by 3 under 100 would be 3, 6, 9, all the way up to 99. There you go, a list of numbers that can be divided by 3 without breaking a sweat.

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

Oh, isn't finding the greatest common factor like finding a happy little tree in a forest? Let's take a look at 72 and 180. We can see that the greatest common factor of these numbers is 36. Just like adding colors to a painting, finding common factors is a way to bring harmony and simplicity to math problems.

2 times 34 =68

Oh, dude, the common factors of 54 and 66 are 1, 2, 3, 6. So, like, these are the numbers that can divide both 54 and 66 without leaving a remainder. Hope that helps, but like, who really cares, right?

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.

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.

Since 118 is a single number, you could say that it shares all of its factors with itself. So the greatest factor of 118 is 118

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.