If I may use an English analogy, factors are like letters and factor strings are like sentences. Factors are numbers that can be multiplied together to create products. Factor strings are factors multiplied together.
The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24
Factor strings for 24 include 2 x 12, 3 x 8, 4 x 6, 2 x 2 x 6, 2 x 3 x 4 and 2 x 2 x 2 x 3
Factors go into numbers. Numbers go into multiples.
Factors go into numbers, numbers go into multiples.
The difference is between factor pairs and distinct factors. With square numbers, one of the factor pairs will be the same number twice. When listing the distinct factors, that number is only listed once.
The factor list will be finite, the multiple list will be infinite.
One way to approach this is to look at the differences between the numbers. The difference between 54 and 75 is 21. The difference between 75 and 96 is 21. The greatest common factor cannot be larger than the smaller difference between the numbers and must be a factor of the difference. The factors of 21 are 1, 3, 7, and 21. The numbers are not divisible by 21, so try the next largest factor. The numbers are not divisible by 7, so try the next largest factor. The numbers are divisible by 3, so the greatest common factor is 3. Another way to determine the greatest common factor is to find all the factors of the numbers and compare them. The factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54. The factors of 75 are 1, 3, 5, 15, 25, and 75. The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96. The common factors are 1 and 3. Therefore, the greatest common factor is 3. The greatest common factor can also be calculated by identifying the common prime factors and multiplying them together. The prime factors of 54 are 2, 3, 3, and 3. The prime factors of 75 are 3, 5, and 5. The prime factors of 96 are 2, 2, 2, 2, 2, and 3. The prime factors in common are a single 3, so the greatest common factor is 3.
37 is prime. Two factors. No strings.
the factors of 32 is 1,2,4,8,16,32.
The GCF is the largest of the common factors.
The greatest common factor is the largest of the common factors.
All numbers have factors. Some factors are prime numbers, some are not.
Prime factors are factors that are prime. For example, 13 is a prime number and 13 is a factor of 26. So that means 13 is a prime factor.
Factors go into numbers, numbers go into multiples.
Factors go into numbers, numbers go into multiples.
Factors go into numbers. Numbers go into multiples.
Factors go into numbers, numbers go into multiples.
Factor strings are multiplication sentences. 2 x 8 = 16 3 x 4 x 5 = 60 are examples of factor strings.
Factors go into numbers, numbers go into multiples.