互相質數的意思、翻譯和例句

是什麼意思

「互相質數」是指兩個整數的最大公因數為 1,這意味著這兩個數沒有共同的正因數。簡單來說,互相質數的數字之間是彼此獨立的,無法被其他數字整除。這個概念在數學中非常重要,尤其是在數論和密碼學中。

依照不同程度的英文解釋

  1. Two numbers that cannot be divided by the same number.
  2. Two numbers that only share the number one as a factor.
  3. Two numbers that do not have any common factors.
  4. Two numbers that are not divisible by the same number except one.
  5. Two numbers that have no common divisors other than one.
  6. Two integers whose greatest common divisor is one.
  7. Two numbers that do not share any prime factors.
  8. Two integers that are coprime, meaning their only common factor is one.
  9. Two integers that are mutually prime, indicating their greatest common divisor is one.
  10. Two integers that are relatively prime, meaning they share no common factors other than one.

相關英文單字或片語的差別與用法

1:Coprime

用法:

在數學中,當兩個整數的最大公因數為1時,這兩個數被稱為互質或相互質數。這個概念在代數和數論中非常重要,因為它涉及到數字之間的關係。

例句及翻譯:

例句 1:

5和9是互質的。

5 and 9 are coprime.

例句 2:

任何質數與其他質數都是互質的。

Any prime number is coprime with another prime number.

例句 3:

12和25是互質的,因為它們沒有共同的因數。

12 and 25 are coprime because they have no common factors.

2:Relatively prime

用法:

這個詞語在數學上用來描述兩個整數之間的關係,當它們的最大公因數是1時,則稱為相對質數。這個概念在數論中常被使用,尤其是在計算分數和簡化方程式時。

例句及翻譯:

例句 1:

8和15是相對質數,因為它們的最大公因數是1。

8 and 15 are relatively prime because their greatest common divisor is 1.

例句 2:

相對質數的概念在數學運算中非常有用。

The concept of relatively prime numbers is very useful in mathematical operations.

例句 3:

如果兩個數是相對質數,它們的乘積的質因數分解不會重複。

If two numbers are relatively prime, their prime factorization will not overlap.

3:Mutually prime

用法:

這個術語與「互質」相似,用於描述兩個整數之間的關係,當它們的最大公因數是1時,它們被認為是互相質數。這在數學中是個重要的概念,特別是在研究數字的性質時。

例句及翻譯:

例句 1:

3和4是互相質數,因為它們沒有共同的因數。

3 and 4 are mutually prime because they have no common factors.

例句 2:

互相質數的數對在數論中有許多應用。

Pairs of mutually prime numbers have many applications in number theory.

例句 3:

要判斷兩個數是否互相質數,可以計算它們的最大公因數。

To determine if two numbers are mutually prime, you can calculate their greatest common divisor.