Here we will explain what 164 mod 70 means and show how to calculate it. 164 mod 70 is short for 164 modulo 70 and it can also be called 164 modulus 70.
Modulo is the operation of finding the Remainder when you divide two numbers. Therefore, when you ask "What is 164 mod 70?" you are asking "What is the Remainder when you divide 164 by 70?".
We will show you two methods of finding 164 mod 70 (164 modulo 70). To differentiate our methods, we will call them the "Modulo Method" and the "Modulus Method".
Before we continue, we remind you of what the different parts of a division problem are called so you can follow along: Dividend / Divisor = Quotient and in this case 164 is the Dividend, 70 is the Divisor, and the answer is called the Quotient.
Furthermore, the Quotient x.y has two parts: x to the left of the decimal point is the Whole part, and y to the right of the decimal point is the Fractional part.
Modulo Method
To find 164 mod 70 using the Modulo Method, we first divide the Dividend (164) by the Divisor (70).
Second, we multiply the Whole part of the Quotient in the previous step by the Divisor (70).
Then finally, we subtract the answer in the second step from the Dividend (164) to get the answer. Here is the math to illustrate how to get 164 mod 70 using our Modulo Method:
164 ÷ 70 ≈ 2.342857
2 × 70 = 140
164 - 140 = 24
Thus, the answer to "What is 164 mod 70?" is 24.
Modulus Method
To find 164 mod 70 using the Modulus Method, we first find the highest multiple of the Divisor (70) that is equal to or less than the Dividend (164).
Then, we subtract the highest Divisor multiple from the Dividend to get the answer to 164 modulus 70 (164 mod 70):
Multiples of 70 are 0, 70, 140, 210, etc. and the highest multiple of 70 equal to or less than 164 is 140. Therefore, to get the answer:
164 - 140 = 24
Thus, once again, the answer to "What is 164 mod 70?" is 24.
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