421 and 427, when divided by the same number, leave the same remainder 1. How many numbers can be used as…
421 and 427, when divided by the same number, leave the same remainder 1. How many numbers can be used as the divisor in order to get the same remainder 1?
1
2
3
4
Solution
Subtracting the remainder 1 from each: 420 and 426. The divisor must divide both 420 and 426. Common factors of $420 = 2^2 \times 3 \times 5 \times 7$ and $426 = 2 \times 3 \times 71$ are 2, 3 and 6. The divisor must also be greater than the remainder 1, which all three satisfy. Hence 3 numbers can be used as the divisor.