Factors could be thought of as the atoms of the number,since factor pairs multiply together to make the number. Every factor has a partner.
Suppose that each number in the table is divided by 7 to produced a quotient and a remainder.
What is the same about the results of the division in each row? Common multiples and the LCM An important way to compare two numbers is to compare their lists of multiples. Let us write out the first few multiples of 4, and the first few multiples of 6, and compare the two lists. The numbers that occur on both lists have been circled, and are called common multiples.
The common multiples of 6 and 8 are 0, 12, 24, 36, 48,… Apart from zero, which is a common multiple of any two numbers, the lowest common multiple of 4 and 6 is These same procedures can be done with any set of two or more non-zero whole numbers.
A common multiple of two or more nonzero whole numbers is a whole number that a multiple of all of them. The lowest common multiple or LCM of two or more whole numbers is the smallest of their common multiples, apart from zero.
Hence write out the first few common multiples of 12 and 16, and state their lowest common multiple.
Hence write down the LCM of 12, 16 and 24? Solution a The multiples of 12 are 12, 24, 36, 48, 60, 72, 84, 96,,… The multiples of 16 are 16, 32, 48, 64, 80, 96,,… Hence the common multiples of 12 and 16 are 48, 96, ,… and their LCM is Two or more nonzero numbers always have a common multiple — just multiply the numbers together.
But the product of the numbers is not necessarily their lowest common multiple. What is the general situation illustrated here? Solution The LCM of 9 and 10 is their product The common multiples are the multiples of the LCM You will have noticed that the list of common multiples of 4 and 6 is actually a list of multiples of their LCM Similarly, the list of common multiples of 12 and 16 is a list of the multiples of their LCM This is a general result, which in Year 7 is best demonstrated by examples.
In an exercise at the end of the module, Primes and Prime Factorisationhowever, we have indicated how to prove the result using prime factorisation. This can be restated in terms of the multiples of the previous section: On the other hand, zero is the only multiple of zero, so zero is a factor of no numbers except zero.
These rather odd remarks are better left unsaid, unless students insist. They should certainly not become a distraction from the nonzero whole numbers that we want to discuss.Prime Factors 1. There are 13 flavors at a local ice cream parlor.
Is the number 13 a prime number or a composite number? If it is composite, write the number as the product of prime numbers. 3.
Sydney used divisibility rules to show that the number is composite. What will she write when she writes the number as the product of prime numbers?
5. Write all the factors of the number 1) 30 2) 31 3) 45 4) 87 Prime and Composite Numbers: A prime number is a whole number that is greater than 1 and has exactly two whole number factors, 1 and itself A composite number is a whole number that is greater than 1 and has more than two whole number factors.
Given that $ = 8^4 - 1$ write $$ as a product of its prime factors. I know how I could separate $$ into prime factors however I'm not sure how I could use $8^4 - 1$ to help me.
May 14, · Write the prime factor in the left column and write your answer across from it in the right column. As noted above, even numbers are especially easy to start factoring because their smallest prime factor will always be 2. Odd numbers, on the other hand, will have smallest prime factors Views: K.
The prime factorization of 70 is 2 times 5 times 7. Multiplying these three prime numbers together makes 70, and this is the only unique combination of prime numbers that equals A prime number is a positive integer that only has two positive factors: the number itself and the number one.
48 and 60 have to be expressed as a product of their prime factors. Write each of the numbers as a product of a prime and another number starting with the smallest prime number 2 and moving to.