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Factoring and Multiples
This category should include questions about greatest common factors and lowest common multiples.
63,380 Questions
What is the LCM of 124 and 200?
Oh, dude, the least common multiple (LCM) of 124 and 200 is 3100. It's like the smallest number that both 124 and 200 can divide into evenly. So, if you were throwing a party and needed to buy snacks in packs of 124 and 200, you'd want to get 3100 of each to make sure you have enough for everyone.
What is the prime factor tree of 98175?
To find the prime factor tree of 98175, we start by dividing it by the smallest prime number, which is 3. 98175 divided by 3 is 32725. Then, we divide 32725 by 5 to get 6545. Continuing this process, we find that the prime factor tree of 98175 is 3 x 5 x 5 x 7 x 11 x 11.
How do you find prime factors?
To determine the prime factors of a number:
Try to divide the number by the lowest prime number, which is 2. If it divides evenly mark that number down as one of the prime factors, and continue with the result, trying to divide that prime factor into it. Continue dividing that prime factor into the results until it no longer divides evenly. If it does not divide evenly, move to the next lowest prime number and repeat the process until you have a result that is a prime number. Now you have all the prime factors.
Example: Find the prime factors of 128.
The prime factors are in bold.
128 ÷ 2 = 64
64 ÷ 2 = 32
32 ÷ 2 = 16
16 ÷ 2 = 8
8 ÷ 2 = 4
4 ÷ 2 = 2 which is a prime factor and thus the final prime factor.
Therefore, the prime factors of 128 are 2, 2, 2, 2, 2, 2, and 2; the prime factorization is 2 x 2 x 2 x 2 x 2 x 2 x 2.
Example: Find the prime factors of 108.
108 ÷ 2 = 54
54 ÷ 2 = 27
27 is not divisible by 2, so try 3.
27 ÷ 3 = 9
9 ÷ 3 = 3 which is a prime factor and thus the final prime factor.
Therefore the prime factors of 108 are 2, 2, 3, 3, and 3; the prime factorization is 2 x 2 x 3 x 3 x 3.
Example: Find the prime factors of 1463.
1463 is not divisible by 2 or 3 or 5, but it is divisible by 7.
1463 ÷ 7 = 209
209 is not divisible 7, so try the next prime number, which is 11.
209 ÷ 11 = 19 which is a prime factor and thus the final prime factor.
Therefore, the prime factors of 1463 are 7, 11, and 19; the prime factorization is 7 x 11 x 19.
Another way to determine the prime factors is to use a factor tree. To make a factor tree, find two numbers whose product is the given number. Then, if those numbers are not prime, do the same for them. Continue until all numbers are prime.
Example: Find the prime factors of 54 using a factor tree.
54
6 x 9
2x3 x 3x3
Therefore, the prime factors of 54 are 2, 3, 3, and 3; the prime factorization is 2 x 3 x 3 x 3.
For other examples of factor trees, see the related question on factoring terminology.
you find it by using exponents and by dividing the two numbers
you do a mutiple of that to get the number you re factoring by then make prime factor tree
What are the factors of 30 75 and 120?
The factors of 30 are: 1, 2, 3, 5, 6, 10, 15, and 30.
The prime factors of 30 are: 2, 3, and 5.
The factors of 75 are: 1, 3, 5, 15, 25, and 75.
The prime factors of 75 are: 3 and 5.
The factors of 120 are: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120.
The prime factors of 120 are: 2, 3, and 5.
What are the first three multiples of 5?
The first three multiples of 5 are 5, 10, and 15. A multiple of a number is the result of multiplying that number by an integer. In this case, the multiples of 5 are obtained by multiplying 5 by 1, 2, and 3, respectively.
What is the lowest common multiple of 360 and 750?
The least common multiple of the integers from 2 to 1000 is the product of all those numbers, or 1000!. Since the LCM of any consecutive integers is their product, the LCM of all integers between 2 and 1000 must by 2*3*4*5*...*998*999*1000.
What is the greatest common factor of 450 and 750?
The greatest common factor (GCF) of two numbers is the largest number that divides both numbers evenly. To find the GCF of 450 and 750, you can list the factors of each number and identify the greatest one they have in common. The factors of 450 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, and 450. The factors of 750 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 125, 150, 250, 375, and 750. The greatest common factor of 450 and 750 is 150.
What are the common multiples of 6 and 11?
Oh, dude, common multiples? That's like when two numbers are hanging out together and they're like, "Hey, let's find some numbers we both like." So, for 6 and 11, their common multiples would be like 66, 132, 198, and so on. It's just like finding a common interest, but with numbers.
What is 38 rounded to the nearest whole number?
When rounding 38 to the nearest whole number, you look at the digit in the ones place, which is 8. Since 8 is greater than or equal to 5, you round up. Therefore, 38 rounded to the nearest whole number is 40.
What is the greatest common multiple of 120 and 200?
Well, isn't that a happy little question! To find the greatest common multiple of 120 and 200, we first need to find the multiples of each number. The multiples of 120 are 120, 240, 360, 480, and so on, and the multiples of 200 are 200, 400, 600, 800, and so forth. The greatest common multiple they share is 600, which is a beautiful number that brings them together in harmony.
What is the highest common factor of 735 and 2625?
The highest common factor (HCF) of two numbers is the largest positive integer that divides both numbers without leaving a remainder. To find the HCF of 735 and 2625, you can use the Euclidean algorithm or prime factorization method. In this case, the prime factorization of 735 is 3 x 5 x 7^2 and the prime factorization of 2625 is 3^2 x 5^2 x 7. The common factors between the two numbers are 3 and 5, so the HCF of 735 and 2625 is 15.
What is 63 as a product of prime factors in index form?
To express 63 as a product of prime factors in index form, we first need to find the prime factors of 63. 63 can be factored as 3 x 3 x 7. This can be written in index form as 3^2 x 7. Therefore, 63 as a product of prime factors in index form is 3^2 x 7.
What is the hcf of 60 72 and 90?
Well, darling, the highest common factor of 60, 72, and 90 is 6. So, if you were wondering which number can divide all three of those numbers without leaving a remainder, it's good ol' 6. Hope that clears things up for you!
What is the least common multiple of 7 14 and 18?
Well, honey, the least common multiple of 7, 14, and 18 is 126. So, if you're looking for a number that all three of those divas can agree on without any drama, 126 is your winner. Now go forth and conquer those multiples like the math royalty you are!
What are the multiples of 4 and it and factor 7 between 48 and 58?
Oh, dude, multiples of 4 are like 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56. And like, the factors of 7 between 48 and 58 are 49 and 56. So, there you have it, my friend.
What is the highest common factor of 55 121 and 132?
To find the highest common factor (HCF) of 55, 121, and 132, we first need to find the prime factors of each number. The prime factors of 55 are 5 and 11, the prime factors of 121 are 11 and 11, and the prime factors of 132 are 2, 2, 3, 11. To find the HCF, we look for the common prime factors among the three numbers, which are 11. Therefore, the highest common factor of 55, 121, and 132 is 11.
What is the greatest common factor of 91 and 259?
Oh, isn't that a happy little math question! Let's find the greatest common factor of 91 and 259. We start by finding the factors of each number and then identifying the largest number that both 91 and 259 can be divided by evenly. Just like painting a beautiful landscape, with a little patience and some gentle math strokes, we'll find that the greatest common factor of 91 and 259 is 13.
No, 4 is not divisible by 348. In order for a number to be divisible by another number, the remainder of the division operation must be zero. When you divide 4 by 348, the remainder is 4, which means 4 is not divisible by 348.
What is the HCF of 882 and 3150 using continued division method?
882/2 = 441/3 = 147/3 = 49/7 = 7/7 = 1
3150/2 = 1575/3 = 525/3 = 175/5 = 35/5 = 7/7 = 1
2 x 3 x 3 x 7 x 7 = 882
2 x 3 x 3 x 5 x 5 x 7 = 3150
2 x 3 x 3 x 7 = 126, the GCF
How many multiples of 10 are there from 20 to 150?
20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150.
The 24 factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360.
The factor pairs of 360 are (1, 360), (2, 180), (3, 120), (4, 90), (5, 72), (6, 60), (8, 45), (9, 40), (10, 36), (12, 30), (15, 24), and (18, 20).
The prime factorization for 360 = 2³×3²×5
What is the greatest common factor of 120 and 135?
To find the greatest common factor (GCF) of 120 and 135, we need to determine the largest number that divides both 120 and 135 without leaving a remainder. One way to find the GCF is to list the factors of each number and identify the greatest one they have in common. The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120. The factors of 135 are 1, 3, 5, 9, 15, 27, 45, and 135. The greatest common factor of 120 and 135 is 15.
What is the greatest common factor of 504 and 588?
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 504 and 588 is 84
