(Surely Christianity doesn't have a monopoly on numeral-based systems of divination, though?)
It doesn't! Judaism most assuredly has its own version, and I'm quite sure other cultures do too. The Jewish version is, of course, based more on the Hebrew alphabet, and has different ideas about lucky numbers and so on. The simplest one to mention and explain is 18: the Hebrew letters representing it (there's a whole system for how to write numbers in Hebrew letters) are י"ח, yud and khet. Flip the letters, and you get the word חי, khai, which means life! So it's a very popular number, especially for things like charitable donations - you see things like High Holidays synagogue donation options being in multiples of 18, and I think I've seen the same for a Jewish high school. The minimum donation is often 18 (in whichever currency - I was about to add a dollar sign, but I expect just about any currency sign would be applicable).
Another is 3. A lot of basic Jewish concepts/tenets seem to come in threes, one of the most famous of which being...one I think we actually discussed once, since you knew a version of it as a choir song and it turned out to have changed the words! In rough translation: "the world relies [literally: "stands"] on three things: on Torah [either the study of it or the moral and ethical rules encompassed in both the Bible and all the writings and teachings that are based on it], on worship [literally "work", in this context meaning roughly "doing things that serve G-d"], and on gmilut khassadim, גמילות חסדים [generally translated, iirc, as...acts of loving-kindness? Dictionary says "charity, benevolence", which sounds about right]."
There are other things that come in threes, too - the main one coming to mind right now is a famous quote from the Mishna, in Pirkei Avot (uh... Chapters of the Fathers? Let me just. Look up the common translation. ...oh my gosh, it actually is translated as that. Alright, then! An alternate is Ethics of the Fathers, which I think is more familiar to me. The first is the literal translation, while the second more accurately describes both the contents and the fact that it's a part of the Mishna, which is a whole bunch of rabbinic Jewish ethics written down about as concisely as possible. Why concisely? Well, this was the Oral Torah, which wasn't supposed to be written down. However, there was a fear that it would be lost, and so Rabbi Yehuda HaNasi (Rabbi Judah the Prince) wrote it down rather sparingly. This is why we have the Talmud, actually: it's basically centuries' worth of interpretations of the Mishna, plus applications of it (theoretical and practical) and stories about the people debating about it all for good measure. Very, very interesting.
And I've been sidetracked. This is...I think the first teaching in Pirkei Avot, actually.
...it is not: it's the sixth. However, there are a couple of teachings before it which also come in threes!
Moses received the Torah at Sinai and transmitted it to Joshua, Joshua to the elders, and the elders to the prophets, and the prophets to the Men of the Great Assembly. They said three things: Be patient in [the administration of] justice, raise many disciples and make a fence round the Torah.
Shimon the Righteous was one of the last of the men of the great assembly. He used to say: the world stands upon three things: the Torah, the Temple service, and the practice of acts of piety. (An alternate translation of the one I talked about before! I translated the second bit as "worship" rather than "Temple service" because that's what it's come to mean in the absence of the Temple; but the Mishna was codified much, much closer to the destruction of the Second Temple, so this translation makes sense in the original context, even though the concept had likely already expanded to service of G-d through prayer, ritual actions, and good deeds, given that's what rabbinic Judaism did - in the wake of the destruction, it took Judaism and reworked it into something that could be practiced anywhere in the world, by means of, primarily, finding ways to substitute prayer for Temple services [which made it more accessible both location-wise and across things like social class] and I think more or less setting up rabbis as perhaps a little more authoritative/leaders than they were when the priests were active, though they were already scholars and community leaders at the time of the destruction, as far as I know.)
Joshua ben Perahiah and Nittai the Arbelite received [the oral tradition] from them. Joshua ben Perahiah used to say: appoint for thyself a teacher, and acquire for thyself a companion and judge all men with the scale weighted in his favor. (Finally, the one I was looking for! Pretty self-explanatory: find a mentor, find a peer you can rely on, and don't let yourself be biased against others in judgement, but rather try to see the good in them. Or at least, that's one interpretation ;) I'm very, very sure there are others.)
There are a whole bunch more after this one that use the three things structure; I spotted two or three in the following five or so alone! I'll stop quoting here, though. All three quoted translations come from here: https://www.sefaria.org/Pirkei_Avot.1?lang=bi I'm not sure which English translation they're using, but it's a reputable site. They also give a little introduction:
Composed in Talmudic Israel (c.190 - c.230 CE). Avot (Fathers) belongs to the fourth order [section of the Mishna, and therefore also the Talmud, later on - I believe the Talmud dates to about 500-800 CE in terms of much of the writing and the final codification; it encompasses the ideas and dramatis personae of...I think it's five or so generations of scholars], Nezikin (The Order of Damages) and presents the laws of interactions between Jews and Gentiles and/or idolaters (from a Jewish perspective) [as well as some general ethics and laws/ideas about interactions between Jews and other Jews, or Jews and the world, as you've seen]. It has five chapters. -same page, drop down piece at the top.
Another quick thing to say about Hebrew numerology is, in perhaps a simpler form...the date! Today turns out to be, in the Hebrew/Jewish calendar (lunar-solar, has its own set of twelve months which are...mostly 29 days long, I think? Can't remember right now), ב׳ בשבט תשפ״א - in translation, the 2nd day of Shvat [/Shevat], 5781. Bet, ב, is the second letter of the Hebrew alphabet and thus corresponds to the number 2 (11 is where the system starts pairing letters together instead of just continuing on down the alphabet. 15 suddenly switches from what's been, essentially, 10+x to 9+6, so as to avoid spelling out one version of G-d's name, which would mean the paper it's written on has to be buried instead of thrown away or destroyed in a normal way. 16 does the same, with the letters for 9 and 7, presumably because yud and vav, the letters for ten and six, are also used in the YHVH (yud hey vav hey) name in the Tanakh, though that's an educated guess - if anyone ever told me, I've long since forgotten. I don't even remember getting an explanation for 15, just that I memorized the change).
Anyway. Continuing on: Shvat, commonly anglicized as Shevat although the E is very much...swallowed, basically, in the Hebrew pronunciation, is the fifth month under the modern system (which takes Tishrei as the first month of the year, since it has Rosh Hashanah, the Jewish New Year, in it). In the ancient system, Nissan was the first month; that's when Passover is celebrated. It was the first month for a long time because it held the date of the Exodus from Egypt, and thus the (renewed) beginning of the Jewish people, though that's an anachronistic term in context (at that point, we're technically talking about Israelites). I don't remember why it was changed, or exactly when, though I expect Rosh Hashanah was a factor in the logic (there are actually...four, I think, new years as laid out in the Talmud! IIRC, there's the new year of the year itself, the new tax/financial year, the new agricultural year, and...hrm. Blanking on the fourth for now). Under the ancient system, Shvat would have been the...eleventh month? Yes, the eleventh month.
And then we get to 5781, תשפ"א. Uh. Basically, at this point we're getting into letters that stand for specific large numbers. I no longer really know this off the top of my head. I do remember that the last few letters of the alphabet correspond to numbers in the hundreds, though. פ, pey must be 80; א, aleph is the first letter of the alphabet and corresponds to 1. ש, shin, and ת, tav, are the final two letters of the alphabet (in that order). My memory claims they correspond to 300 and 400 respectively. If the currently surfacing vague memory that the 5,000 is added to the date through inside knowledge rather than written out is accurate, then this makes perfect sense - the letters here actually show 781, written as 400+300+80+1 (plus signs implied only). Add them together, and you've got 781! And then add in 5,000 years since...it must be the date of...Creation? Hrm. Yeah, seems it's 5,000 years since the date of Creation as calculated by Rabbi Yossi ben Halafta in the second century, CE: https://www.myjewishlearning.com/article/counting-the-years/ According to the article, [t]o this day, those Jews who believe the biblical accounting of time to be literal still accept Rabbi Yossi’s calculation, dating Creation to the year 3761 B.C.E. Others claim that the date is figurative, symbolic, or holds esoteric meaning. This makes a good deal of sense, considering both the varied interactions of Jews with science and modernity, and the fact that "two Jews, three opinions" is an idiom I keep ready to hand because it's extremely applicable. Either way, that's when we're counting from to get 5781 (which will last roughly from September 2020 to September 2021 - Tishrei falls in September/October, with an occasional few days landing in August).
And with that, I think I'm done for now. Sources: my education and degree, plus the couple that I linked. Hopefully that was both informative and interesting! :)
PS: As ever, I'm happy to discuss further when it comes to this or other religious/cultural topics, time and energy permitting :) ...er, very much not in a proselytizing sense: that's actively forbidden in Jewish religious law (halacha), and I stick to it. I just enjoy cultural exchange and delving back into different aspects of my field now and then. Presenting these concepts understandably to people who don't have the same background knowledge/context is an interesting challenge, too, and generally a useful thing to practice! Especially since my current job partially relies on being able to present information (mostly historical) to people who might well know nothing about it, or very, very little.