1. **State the problem:** Find the greatest common factor (GCF) of 140392 and 490. 2. **Recall the formula:** The GCF of two numbers is the largest number that divides both without leaving a remainder. 3. **Prime factorization:** - Factor 140392: $$140392 \div 2 = 70196$$ $$70196 \div 2 = 35098$$ $$35098 \div 2 = 17549$$ 17549 is not divisible by 2; check next primes. $$17549 \div 7 = 2507$$ (since 7*2507=17549) $$2507 \div 7 = 358.14...$$ not exact, try 13: $$2507 \div 13 = 193$$ (exact) 193 is prime. So prime factors of 140392 are: $$2^3 \times 7 \times 13 \times 193$$ - Factor 490: $$490 \div 2 = 245$$ $$245 \div 5 = 49$$ $$49 = 7^2$$ So prime factors of 490 are: $$2 \times 5 \times 7^2$$ 4. **Find common prime factors with lowest powers:** - Common primes: 2 and 7 - For 2: minimum power is $2^1$ - For 7: minimum power is $7^1$ 5. **Calculate GCF:** $$GCF = 2^1 \times 7^1 = 2 \times 7 = 14$$ **Final answer:** The greatest common factor of 140392 and 490 is **14**.