You have to be level 40 for starters.
Then you get 15 for the Daily Crucible and Daily Heroic mission once each day (some missions have been bugged forever and do not reward on completion they send the marks to the postmaster a week later)
You'll see these in the Director screen, where you select destinations, down in the lower left corner.
You also get 10 for Weekly Heroic Strikes (only the first 1 - 3 strikes, not 100% sure how many strikes give each week as I haven't bothered with the strike list in over a year)
Weekly Crucible modes (like mayhem clash) give 10 each for first three wins each week (only winning team gets marks here)
The nightfall might, not sure haven't looked at that in ages either.
Some quests may reward a few marks as well.
Dismantled Legendary gear gives 3-5 I believe rng based.
English
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For dismantling mine have always been 3
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If the gear has all modes unlocked, no purchase necessary, it will dismantle into 5 marks. Otherwise 3. Same with exoctics, fully upgraded will yield 2 exotic shards, in upgraded will yield 1
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When you dismantle are they new or do you fill up their xp first? I know stuff with full xp gives better mats/light/shards when dismantled, maybe that's the same with marks too? I know I've received 5 before.
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To be honest probably a mix of both and probably never noticed