When we talk about numbers, we often come across the term "divisors." A divisor is a number that can divide another number without leaving a remainder. This means when you divide a number (let’s call it the dividend) by a divisor, you get a whole number as the result, which is known as the quotient. Understanding divisors can help in a number of mathematical concepts, including fractions, factors, and even in finding the greatest common divisor.
To grasp the concept of division, we should understand three key terms: the dividend, the divisor, and the quotient. The dividend is the number we want to divide, the divisor is the number we are dividing by, and the quotient is the result we get. For example, let’s use the number 71:
If we divide 71 by 1, we write it like this:
71 / 1 = 71
Here, 71 is the dividend, 1 is the divisor, and 71 is also the quotient.
Now, let’s calculate the divisors of the number 71. To find all the divisors, we need to divide 71 by every whole number starting from 1 up to 71 itself, to see if the result is a whole number. Here’s how we do this step-by-step:
- Start with the number 1 and go up to 71.
- For each whole number, divide 71 by that number.
- Check if the result (the quotient) is a whole number (which means there is no remainder).
Let’s do this step by step for the number 71:
- 1: 71 / 1 = 71 (whole number)
- 2: 71 / 2 = 35.5 (not a whole number)
- 3: 71 / 3 ≈ 23.67 (not a whole number)
- 4: 71 / 4 = 17.75 (not a whole number)
- 5: 71 / 5 = 14.2 (not a whole number)
- 6: 71 / 6 ≈ 11.83 (not a whole number)
- 7: 71 / 7 ≈ 10.14 (not a whole number)
- 8: 71 / 8 = 8.875 (not a whole number)
- 9: 71 / 9 ≈ 7.89 (not a whole number)
- 10: 71 / 10 = 7.1 (not a whole number)
- 11: 71 / 11 ≈ 6.45 (not a whole number)
- 12: 71 / 12 ≈ 5.92 (not a whole number)
- 13: 71 / 13 ≈ 5.46 (not a whole number)
- 14: 71 / 14 ≈ 5.07 (not a whole number)
- 15: 71 / 15 ≈ 4.73 (not a whole number)
- 16: 71 / 16 ≈ 4.44 (not a whole number)
- 17: 71 / 17 ≈ 4.18 (not a whole number)
- 18: 71 / 18 ≈ 3.94 (not a whole number)
- 19: 71 / 19 ≈ 3.74 (not a whole number)
- 20: 71 / 20 = 3.55 (not a whole number)
- 21: 71 / 21 ≈ 3.38 (not a whole number)
- 22: 71 / 22 ≈ 3.23 (not a whole number)
- 23: 71 / 23 ≈ 3.09 (not a whole number)
- 24: 71 / 24 ≈ 2.96 (not a whole number)
- 25: 71 / 25 = 2.84 (not a whole number)
- 26: 71 / 26 ≈ 2.73 (not a whole number)
- 27: 71 / 27 ≈ 2.63 (not a whole number)
- 28: 71 / 28 ≈ 2.54 (not a whole number)
- 29: 71 / 29 ≈ 2.45 (not a whole number)
- 30: 71 / 30 ≈ 2.37 (not a whole number)
- 31: 71 / 31 ≈ 2.29 (not a whole number)
- 32: 71 / 32 ≈ 2.22 (not a whole number)
- 33: 71 / 33 ≈ 2.15 (not a whole number)
- 34: 71 / 34 ≈ 2.09 (not a whole number)
- 35: 71 / 35 ≈ 2.03 (not a whole number)
- 36: 71 / 36 ≈ 1.97 (not a whole number)
- 37: 71 / 37 ≈ 1.92 (not a whole number)
- 38: 71 / 38 ≈ 1.86 (not a whole number)
- 39: 71 / 39 ≈ 1.82 (not a whole number)
- 40: 71 / 40 ≈ 1.78 (not a whole number)
- 41: 71 / 41 ≈ 1.73 (not a whole number)
- 42: 71 / 42 ≈ 1.69 (not a whole number)
- 43: 71 / 43 ≈ 1.65 (not a whole number)
- 44: 71 / 44 ≈ 1.61 (not a whole number)
- 45: 71 / 45 ≈ 1.58 (not a whole number)
- 46: 71 / 46 ≈ 1.54 (not a whole number)
- 47: 71 / 47 ≈ 1.51 (not a whole number)
- 48: 71 / 48 ≈ 1.48 (not a whole number)
- 49: 71 / 49 ≈ 1.45 (not a whole number)
- 50: 71 / 50 = 1.42 (not a whole number)
- 51: 71 / 51 ≈ 1.39 (not a whole number)
- 52: 71 / 52 ≈ 1.36 (not a whole number)
- 53: 71 / 53 ≈ 1.34 (not a whole number)
- 54: 71 / 54 ≈ 1.31 (not a whole number)
- 55: 71 / 55 ≈ 1.29 (not a whole number)
- 56: 71 / 56 ≈ 1.27 (not a whole number)
- 57: 71 / 57 ≈ 1.24 (not a whole number)
- 58: 71 / 58 ≈ 1.22 (not a whole number)
- 59: 71 / 59 ≈ 1.20 (not a whole number)
- 60: 71 / 60 ≈ 1.18 (not a whole number)
- 61: 71 / 61 ≈ 1.16 (not a whole number)
- 62: 71 / 62 ≈ 1.14 (not a whole number)
- 63: 71 / 63 ≈ 1.13 (not a whole number)
- 64: 71 / 64 ≈ 1.11 (not a whole number)
- 65: 71 / 65 ≈ 1.09 (not a whole number)
- 66: 71 / 66 ≈ 1.08 (not a whole number)
- 67: 71 / 67 ≈ 1.06 (not a whole number)
- 68: 71 / 68 ≈ 1.04 (not a whole number)
- 69: 71 / 69 ≈ 1.03 (not a whole number)
- 70: 71 / 70 ≈ 1.01 (not a whole number)
- 71: 71 / 71 = 1 (whole number)
From our calculations, the only whole numbers we found were when we divided by 1 and 71. Thus, the divisors of 71 are:
Divisors of 71: 1, 71
In conclusion, the divisors of a number are critical to understanding its structure and relationships with other numbers. For the number 71, the only divisors are:
1, 71