Number system

Any number that leaves a remainder of 3 when divided by 7 can be written as 7k + 3. Depending on whether k is even or odd, dividing this number by 14 will result in a remainder of either 3 or 10. Assuming the remainder can only be 3 overlooks the case where k is odd, leading to an incomplete answer.

The last digit of powers of 7 follows a repeating cycle of four: 7, 9, 3, and 1. Since the exponent 100 is perfectly divisible by 4, the last digit must be the fourth number in the cycle, which is 1. Option C is incorrect because 7 only appears when the exponent leaves a remainder of 1

The greatest common divisor (GCD) is found by multiplying the lowest powers of common prime factors, which are 2^2 * 3 = 12. A diagram for this topic isn't available yet — the worked example below walks the same reasoning step by step.

• !The greatest common divisor (GCD) is found by multiplying the lowest powers of common prime factors, which are 2^2 * 3 = 12.
• !Option C is incorrect because 7 only appears when the exponent leaves a remainder of 1

Answer each from memory — you'll see instantly whether you're right and why.

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