Prime factorization is one of the essential concepts in mathematics. It is the process of breaking down a composite number into its prime factors. In this article, we will discuss the prime factorization of the number 70.
What is Prime Factorization?
Prime factorization involves finding the prime numbers that multiply together to give a composite number. A composite number is a positive integer that has more than two factors. For example, the number 70 is a composite number because it has four factors: 1, 2, 5, and 70.
Method of Prime Factorization
To find the prime factorization of a number, we divide it by its smallest prime factor. We continue dividing the result by its smallest prime factor until we get a quotient that is a prime number. Then, we write down all the prime factors that we used in the division.
Prime Factors of 70
To find the prime factors of 70, we start by dividing it by the smallest prime number, which is 2. We get 35 as the quotient. Since 35 is not a prime number, we continue by dividing it by 5, which is the smallest prime factor of 35. We get 7 as the quotient. Since 7 is a prime number, we stop here. Therefore, the prime factorization of 70 is 2 x 5 x 7.
Explanation of Prime Factorization
The prime factorization of a number is unique. It means that every composite number can be expressed as a product of prime numbers in only one way. The prime factorization of a number can help us find its common factors, highest common factor, and lowest common multiple.
Common Factors of 70
The common factors of two or more numbers are the factors that they have in common. To find the common factors of 70, we list down all its factors: 1, 2, 5, 10, 14, 35, and 70. Then, we list down all the factors of another number, for example, 30: 1, 2, 3, 5, 6, 10, 15, and 30. The common factors of 70 and 30 are 1, 2, 5, and 10.
Highest Common Factor of 70
The highest common factor (HCF) of two or more numbers is the highest factor that they have in common. To find the HCF of 70 and 30, we list down all their factors and find the highest common factor: 1, 2, 5, 10, 14, 35, and 70 for 70; 1, 2, 3, 5, 6, 10, 15, and 30 for 30. The HCF of 70 and 30 is 10.
Lowest Common Multiple of 70
The lowest common multiple (LCM) of two or more numbers is the smallest multiple that they have in common. To find the LCM of 70 and 30, we list down their multiples until we find the smallest common multiple: 70, 140, 210, 280, 350, 420, 490, 560, 630, 700, 770, 840, 910, 980, 1050, 1120, 1190, 1260, 1330, 1400 for 70; 30, 60, 90, 120, 150, 180, 210, 240, 270, 300, 330, 360, 390, 420, 450, 480, 510, 540, 570, 600 for 30. The LCM of 70 and 30 is 210.
Conclusion
In conclusion, the prime factorization of 70 is 2 x 5 x 7. Prime factorization is an important concept in mathematics that helps us solve many problems related to factors and multiples. By understanding the prime factorization of a number, we can find its common factors, highest common factor, and lowest common multiple.
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