Reduce 391/667 to lowest terms.

To reduce the fraction 391/667 to its lowest terms, you need to find the Highest Common Factor (H.C.F.) of both the numerator and the denominator and then divide both by that factor.

Step-by-Step Calculation

1. Find the H.C.F. of 391 and 667: The most efficient way to find the H.C.F. of large numbers is using the Euclidean algorithm:

• Divide 667 by 391: 667 = (391 × 1) + 276

• Divide 391 by 276: 391 = (276 × 1) + 115

• Divide 276 by 115: 276 = (115 × 2) + 46

• Divide 115 by 46: 115 = (46 × 2) + 23

• Divide 46 by 23: 46 = (23 × 2) + 0

When the remainder is 0, the divisor is the H.C.F. Therefore, the H.C.F. is 23.

2. Reduce the fraction: Divide both the numerator and the denominator by 23:

• Numerator: 391 / 23 = 17

• Denominator: 667 / 23 = 29

The fraction in its lowest terms is 17/29.