public static Fraction simplifyFraction(Fraction f)
			throws ArithmeticException {
		int denominator = f.getDenominator();
		int numerator = f.getNumerator();
		int sign = 1;
		int smaller;
		int factorLimit; // the largest of the lower of potential factor pairs

		// check for division by zero
		if (denominator == 0) {
			throw new ArithmeticException("division by zero");
		}

		// check the sign and keep only the magnitude until the return
		if ((long) denominator * (long) numerator < 0) {
			denominator = Math.abs(denominator);
			numerator = Math.abs(numerator);
			sign = -1;
		}

		// check which number is larger and whether the larger is an even
		// multiple of the smaller

		if (numerator < denominator) {
			if (denominator % numerator == 0) {
				return new Fraction(1 * sign, denominator / numerator);
			}
			smaller = numerator;
		} else {
			if (numerator % denominator == 0) {
				return new Fraction(numerator / denominator * sign, 1);
			}
			smaller = denominator;
		}

		factorLimit = (int) Math.abs(smaller);

		for (int i = 2; i < factorLimit; i++) {
			int factorCandidate1 = i;
			int factorCandidate2 = (smaller / i);

			if (numerator % factorCandidate1 == 0
					&& denominator % factorCandidate1 == 0) {
				numerator /= factorCandidate1;
				denominator /= factorCandidate1;
			}
			if (denominator % factorCandidate2 == 0
					&& numerator % factorCandidate2 == 0) {
				numerator /= factorCandidate2;
				denominator /= factorCandidate2;
			}
		}

		return new Fraction(numerator * sign, denominator);

	}