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What is the lowest common multiple of 7 12 and 14?
Start by factoring each of the numbers. 7=7 12=2x2x3 14=2x7 Remove the duplicated factors. 7 is duplicated between 7 and 14; so remove one 7. 2 is duplicated between 12 and 14; so remove one 2. Multiply together the remaining factors. 7x2x2x3=84 Answer: 84
9 2 7 - 6 5 7?
Guessing that is: 9 2/7 - 6 5/7 = (8 + 1 + 2/7) - 6 5/7 = (8 + 7/7 + 2/7) - 6 5/7 = 8 9/7 - 6 5/7 = 2 4/7 Alternatively, using improper fractions: 9 2/7 - 6 5/7 = (9x7+2)/7 - (6x7+5)/7 = 65/7 - 47/7 = 18/7 = (2x7+4)/7 = 2 4/7
How do you find the greatest common factor of 210 and 308?
* One method is to factor each number into prime factors, and see what factors they have in common. 210 = 2x105 = 2x5x21 = 2x5x3x7, or 2x3x5x7. 308 = 2x154 = 2x2x77 = 2x2x7x11. The GCF is 2x7 = 14. * Another method (more efficient, especially for larger numbers) is Euclid's algorithm. In this case for example, the greatest common factor of 308 and 210 is the same as the greatest common factor of 210 and 98. This latter number is the remainder of the division of 308 by 210. Continue until one of the numbers is zero. In that case, the other one is the greatest common factor. 308/210 = 1, remainder 98 210/98 = 2, remainder 14 98/14 = 7, remainder 0. The previous remainder (14) is the GCF.
