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Factoring and Multiples
This category should include questions about greatest common factors and lowest common multiples.
63,380 Questions
Which number other than 1 2 8 and 16 divides exactly into 16?
The number 4 divides exactly into 16. This is because 16 divided by 4 equals 4, with no remainder. In general, a number divides exactly into another number if the division results in a whole number quotient without any remainder.
What are the multiples of 13 up to 1000?
The multiples of 13 up to 1,000 are:
13, 26, 39, 52, 65, 78, 91, 104, 117, 130,
143, 156, 169, 182, 195, 208, 221, 234, 247, 260,
273, 286, 299, 312, 325, 338, 351, 364, 377, 390,
403, 416, 429, 442, 455, 468, 481, 494, 507, 520,
533, 546, 559, 572, 585, 598, 611, 624, 637, 650,
663, 676, 689, 702, 715, 728, 741, 754, 767, 780,
793, 806, 819, 832, 845, 858, 871, 884, 897, 910,
923, 936, 949, 962, 975, 988.
What is the LCM of 100 and 180?
The Least Common Multiple (LCM) of 100 and 180 can be found by first determining the prime factorization of each number. The prime factors of 100 are 2^2 * 5^2, and the prime factors of 180 are 2^2 * 3^2 * 5. To find the LCM, we take the highest power of each prime factor that appears in either number, which gives us 2^2 * 3^2 * 5^2 = 900. Therefore, the LCM of 100 and 180 is 900.
What is a common factor of 32 64 and 76?
A common factor of 32, 64, and 76 is a number that divides evenly into all three of these numbers. To find the common factors, we can first find the prime factorization of each number. The prime factorization of 32 is 2^5, the prime factorization of 64 is 2^6, and the prime factorization of 76 is 2^2 * 19. The common factor among these three numbers is 2^2, which is 4.
Write 75 as a product of prime factors?
Prime factorization is the finding which prime number multiply to get to make the original number.
Factors of 75: 1, 3, 5, 15, 25, 75
Prime factors: 3, 5
3 x 5 x 5 = 75
Ah, the Highest Common Factor, isn't that a happy little concept? Let's see, to find the HCF of 260, we can break it down into its prime factors, which are 2 x 2 x 5 x 13. Then, we look for the common factors it shares with other numbers to find the highest one. Remember, there are no mistakes, just happy little accidents in mathematics!
What are all the multiples of 0.24?
The multiples of 0.24 are numbers that can be obtained by multiplying 0.24 by any integer. In other words, the multiples of 0.24 are 0.24, 0.48, 0.72, 0.96, and so on. These multiples form a sequence that increases by 0.24 each time.
To factor the expression 3x^2 - 9x^3, we first need to find the greatest common factor (GCF) of the two terms. The GCF of 3x^2 and 9x^3 is 3x^2. We can factor out 3x^2 from both terms to get 3x^2(1 - 3x). Therefore, the factored form of 3x^2 - 9x^3 is 3x^2(1 - 3x).
What is a prime factorization?
Prime factorization is finding the prime factors you need to multiply together to get the original number. A prime factor is a factor that is a prime number.
Example:
The prime factorization of 30 is 2 x 3 x 5
Prime factorization is breaking a number into smaller prime divisors which multiply to equal the original number.
All composite numbers can be expressed as unique products of prime numbers. This is accomplished by dividing the original number and its factors by prime numbers until all the factors are prime. A factor tree can help you visualize this.
Example: 210
210 Divide by two.
105,2 Divide by three.
35,3,2 Divide by five.
7,5,3,2 Stop. All the factors are prime.
2 x 3 x 5 x 7 = 210
That's the prime factorization of 210.
What is the greatest common factor of 24 45 and 48?
The greatest common factor of 24, 45, and 48 is 3
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.
What is the highest common factor of 56 and 160?
The highest common factor (HCF) of 56 and 160 is the largest number that divides both 56 and 160 without leaving a remainder. To find the HCF, we need to determine the common factors of 56 and 160, which are 1, 2, 4, and 8. The highest common factor of 56 and 160 is 8.
The Highest Common Factor (HCF) of 18 and 30 is the largest positive integer that divides both numbers without leaving a remainder. To find the HCF, we need to determine the common factors of 18 (1, 2, 3, 6, 9, 18) and 30 (1, 2, 3, 5, 6, 10, 15, 30) and identify the largest one they share, which is 6. Therefore, the HCF of 18 and 30 is 6.
What are the multiples of 11 up to 2000?
The multiples of 11 are numbers that can be divided evenly by 11. To find the multiples of 11 up to 2000, we can start by finding the first multiple of 11, which is 11 itself. The next multiples would be 22, 33, 44, and so on. Continuing this pattern, we find that the multiples of 11 up to 2000 are 11, 22, 33, 44, ..., 1988, 1999.
To find two numbers that multiply to -317, we need to consider the factors of -317. The factors of 317 are 1, 11, 29, and 317. Since -317 is negative, the two numbers must have different signs. Therefore, the pair of numbers that multiply to -317 is -1 and 317.
To find two numbers that multiply to 172, we can start by listing the factors of 172: 1, 2, 4, 43, 86, and 172. Since we are looking for two numbers, we pair these factors: 1 x 172, 2 x 86, and 4 x 43. Therefore, the two numbers that multiply to 172 are 4 and 43.
What are the factors of 258 and 344?
Alright, buckle up buttercup. The factors of 258 are 1, 2, 3, 6, 43, 86, 129, and 258. And for 344, we've got 1, 2, 4, 8, 43, 86, 172, and 344. So there you have it, the cold hard truth about the factors of 258 and 344.
What is the greatest common factor of 56 84 and 140?
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 50 and 140 is 10
Oh, what a delightful question we have here! To find out what times what equals 1764, we can break it down into factors. 1764 can be expressed as 42 multiplied by 42. Isn't that just a happy little fact to discover?
Oh, dude, the Highest Common Factor (HCF) of 6 and 30 is like the biggest number that can divide both of them without leaving a remainder. So, you look at the factors of 6 (1, 2, 3, 6) and 30 (1, 2, 3, 5, 6, 10, 15, 30) and find the biggest one they have in common. In this case, it's 6. So, the HCF of 6 and 30 is 6. Easy peasy, lemon squeezy!
What is average of 2.65 2.75 2.80 2.77 2.60 2.65 and 2.68?
To find the average of a set of numbers, you add all the numbers together and then divide by the total count of numbers. In this case, the sum of the numbers 2.65, 2.75, 2.80, 2.77, 2.60, 2.65, and 2.68 is 18.90. Since there are 7 numbers in the set, the average would be 18.90 divided by 7, which equals approximately 2.70.
What are the factors and prime factorization of 690?
To find the factors of 690, we start by dividing 690 by the smallest prime number, which is 2. We get 2 x 345. Continuing this process, we find the prime factorization of 690 to be 2 x 3 x 5 x 23. Therefore, the factors of 690 are 1, 2, 3, 5, 6, 10, 15, 23, 30, 46, 69, 115, 138, 230, 345, and 690.
What is the common factors for 39 and 52?
The common factors for 39 and 52 are the numbers that can evenly divide both 39 and 52 without leaving a remainder. The common factors of 39 are 1, 3, 13, and 39, while the common factors of 52 are 1, 2, 4, 13, 26, and 52. Therefore, the only common factor for both 39 and 52 is 13.
What is the difference between multiple and divisible?
They involve the same relationship. The major difference is grammatical. "Multiple" is a noun, meaning a number that can be divided by another number without a remainder.
"Divisible" is an adjective, meaning capable of being divided by another number without a remainder.
12 is a multiple of 3. In this sentence, the word "multiple" refers to the number 12.
12 is divisible by 3. In this sentence, "divisible" refers to a quality that 12 has.
What is the highest common factor of 40 and 72?
The highest common factor (HCF) of 40 and 72 is the largest number that divides both 40 and 72 without leaving a remainder. To find the HCF, we need to identify the common factors of 40 and 72, which are 1, 2, 4, and 8. The highest common factor of 40 and 72 is 8.
