find lcm and hcf of first 10 whole numbers
Answers
Step-by-step explanation:
Fundamental theorem of Arithmetic
Before stating the theorem, let's have a short recap on the concepts of factors, prime numbers and prime factors.
A Factor of an integer is a second integer that divides the first integer fully leaving zero remainder.
For example, 3 and 4 are two factors of the integer 12.
Secondly,
A prime number is an integer that has only 1 and itself as its factors.
For example, 6 is not a prime number as it has 2 and 3 as factors. But 31 is a prime number as it has only 1 and itself as its factors.
From these two concepts, we can define a prime factor as,
A prime factor is a prime number and is a factor of a second integer.
For example, among the two factors 3 and 4 of 12, 3 is a prime factor but 4 is not, as 4 has 2 as a prime factor. That's why when we express an integer as a product of factors by factorization, we find all the prime factors of the integer. For example, when we factorize 12, we find its three factors as 2, 2 and 3 and express it as the product of these prime factors as,
12=2×2×3.
Now we are ready to state the Fundamental theorem of Arithmetic as,
Every positive integer can be expressed as a product of a unique set of prime factors, where the individual factors may appear in any position in the product.
Reason why fundamental theorem of arithmetic is true
Let's assume the integer N is factorized into two unique set of prime factors as,
N1=a1×a2×c3×b1×b2×b3, and,
Answer:
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Step-by-step explanation:
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