Divides

If p is a nonzero non-unit, we say that p is a prime element if, whenever p divides a product ab, then p divides a or p divides b. Equivalently, an element p is prime if and only if the principal ideal (p) is a nonzero prime ideal.

If a and b are coprime and a divides the product bc, then a divides c. This can be viewed as a generalization of Euclid's lemma.

Some properties of the GCD are in fact easier to see with this description, for instance the fact that any common divisor of a and b also divides the GCD (it divides both terms of ua + vb).

There is no proplastid differentiation—when an algal cell divides, its chloroplast divides along with it, and each daughter cell receives a mature chloroplast.

The twelfth fret divides the string in two exact halves and the 24th fret (if present) divides the string in half yet again.

Almost more than any other issue, the debate over Ukraine divides the GOP along generational and ideological lines — especially as Trump is the leading candidate for the GOP nomination next year.

Amazon packages have been arriving at the doors of Prime customers even faster this year under the company’s new distribution model, which divides the country into eight regions and predominantly ships items from warehouses in those areas.

Among them was retiree Darin Edwards, who divides his time between homes in Quesnel and Langley.

As long as the next phase of Molok Luyok comes with more resources, Ryan Henson with the California Wilderness Coalition is optimistic those divides can be bridged.

Disney Plus also gets credit for its organized Originals tab layout, which divides everything into categories.

Good job doing busy work that further divides us.

He encouraged those in the room to connect with young people and bridge divides across communities.

HEICO divides its operations into two reportable segments: the flight support segment and the electronic technologies segment.

He introduces a world that's "grappling with overpopulation and widening social divides," stated.

In an age of isolation and splintering divides and looming threats on the horizon, embrace poetry and all that it offers.

In many cases, New Jersey’s 12 members of the House split along party lines – but sometimes the divides were more complicated.

In what can only be considered a quirk of how Westmoreland County divides its voting district, 52 of the ward’s voters live in Penn Township yet vote for Penn-Trafford School Board and the Penn Township commissioners in a voting booth in Jeannette.

I see the divides between factions of Americans as that we should all be striving to address.

Israel needs to pause the current legislation to focus on the root cause and find a more sustainable means of addressing this and our many other divides.

It can show just how fully this divides the Seven Kingdoms of Westeros, and bring other characters and houses into the fold some more.