The greatest common factor (GCF) of 21 and 35 is 7. This is determined by listing the prime factorizations of both numbers and then finding the largest number that appears in both lists.
The prime factorization of 21 is 3 x 7, and the prime factorization of 35 is 5 x 7. As 7 appears in both lists, it is the greatest common factor of these two numbers.
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What are 21 and 35 factors?
21 and 35 are both composite numbers, which means they can both be broken down into smaller numbers that multiply together to create the original number.
The factors of 21 are 1, 3, 7, and 21. 3×7=21, so these two numbers are the prime factors of 21. The other factors of 21 can be found by multiplying these prime factors together in any combination.
The factors of 35 are 1, 5, 7, and 35. 5×7=35, so these two numbers are the prime factors of 35. The other factors of 35 can be found by multiplying these prime factors together in any combination.
Does 21 and 35 have a common factor?
Yes, 21 and 35 have a common factor. The greatest common factor (GCF) of 21 and 35 is 7. The factors of 21 are 1, 3, 7, and 21 and the factors of 35 are 1, 5, 7, and 35. There are two numbers (7 and 1) which are common factors of both 21 and 35, and the greatest one is 7, so the GCF of 21 and 35 is 7.
What is the greatest common multiple of 21 and 35?
The greatest common multiple of 21 and 35 is 105. This is because it is the largest number that is the multiple of both 21 and 35. To calculate the greatest common multiple (also known as the highest common factor or greatest common divisor) of two numbers, you can list all the multiples of both numbers and determine the largest one that appears in both lists.
Multiples of 21 are 21, 42, 63, 84, 105, 126, etc. while multiples of 35 are 35, 70, 105, 140, etc. The largest multiple that is in both lists is 105, which is the greatest common multiple of 21 and 35.
How do you find the GCF of 21 35?
To find the Greatest Common Factor (GCF) of 21 and 35, you can use a method known as the “Divisibility and Prime Factorization Method. ” First, start by dividing 21 and 35 by numbers smaller than them, beginning with 2.
Since 2 can’t be evenly divided into 21 or 35, you move on to the next number, 3. When 21 is divided by 3, the result is 7; when 35 is divided by 3, the result is 11. Therefore, 3 is the GCF of 21 and 35.
What are the factors of 35?
The factors of 35 are 1, 5, 7, and 35. When finding the factors of a number, you can divide the number by another number and if there is no remainder, that is a factor. In this case, for 35, when divided by 1, there is no remainder (1 x 35 = 35), so 1 is a factor.
When divided by 5, there is also no remainder (5 x 7 = 35), so 5 is a factor. When divided by 7, there is again no remainder (7 x 5 = 35), so 7 is a factor. Finally, when divided by 35, there is no remainder (35 x 1 = 35), so 35 is a factor.
Therefore, the factors of 35 are 1, 5, 7, and 35.
What is the fastest way to find the GCF?
The fastest way to find the greatest common factor (GCF) of two or more numbers is by using the prime factorization method. This involves writing each number as a product of its prime factors, and then finding the common factors among them.
For example, if you wanted to find the GCF of 18 and 24, the prime factorization would be 18 = 2•3•3 and 24 = 2•2•2•3. Comparing the two prime factorization lists, the common factors are 2 and 3. Therefore, the GCF of 18 and 24 is 6.
How do you calculate GCF?
The greatest common factor (GCF) of a set of numbers is the largest number that evenly divides all of the numbers. To calculate the GCF of a set of numbers, you can use the prime factorization method.
First, find the prime factors of each number. To do this, you would need to list out all of the factors of each number, and then eliminate any composite factors (those with more than two factors). Then, list out all of the prime factors common among the numbers in the set (you can use a Venn diagram to help).
The GCF is the product of all of the common prime factors. If a factor is not common to every number, it does not need to be included in the product.
What does LCM mean in math?
LCM stands for Least Common Multiple. It is an important concept in mathematics that is used to determine the smallest positive whole number that is a multiple of two or more numbers. For example, the LCM of 10 and 15 is 30, because it is the smallest positive multiple of 10 and 15.
The LCM is important for solving many types of problems in math, such as finding the greatest common factor (the largest number that is a factor of two or more numbers) or simplifying fractions. It can also be used to solve equations with several terms that are all factors of multiple numbers.
Is 21 and 12 a co prime number?
Yes, 21 and 12 are co-prime numbers. Co-primes, also known as relatively prime numbers, are two numbers where the only common factor between them is 1. 21 and 12 have no other common factors except for 1, making them co-prime numbers.
For example, their greatest common factor (GCF) is 1, and their least common multiple (LCM) is 84. Since 21 and 12 have no common factors other than 1, they are considered to be co-prime.
Is 35 a prime number and why?
No, 35 is not a prime number because it is divisible by 5 and 7. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Prime numbers can only be divided evenly by 1 and themselves.
Since 35 is divisible by 5 and 7, it cannot be considered a prime number.
