ASVAB CampNumber Properties and Divisibility flashcards
8 cards with the formulas, rules and traps from this lesson. Answer in your head, then flip to check.
Term · 1/8
Factor vs. multiple: what is the difference?
A factor divides a number with no remainder (factors of 12: 1, 2, 3, 4, 6, 12, a finite list). A multiple is the number times a whole number (12, 24, 36, ... without end). Since 4 is a factor of 12, 12 is a multiple of 4.
Term · 2/8
What makes a number prime, and where do 1 and 2 fit?
A prime is a whole number greater than 1 whose only factors are 1 and itself. A composite has more than two factors. The number 1 counts as neither, and 2 is the one even prime.
Rule · 3/8
Divisibility tests for 3, 9, 4 and 8?
3 or 9: the digit sum is divisible by 3 or 9. 4: the last two digits form a multiple of 4. 8: the last three digits form a multiple of 8. Example: 7,128 has digit sum 18 and ends in 128, so 3, 9, 4 and 8 all divide it.
Rule · 4/8
How do you test divisibility by 6 and by 11?
6: the number must be even and pass the test for 3. 11: from the left, alternately subtract and add the digits; a result of 0 or a multiple of 11 means divisible. Example: 3,729 gives 3 − 7 + 2 − 9 = −11, so 11 divides it.
Formula · 5/8
How do you get the GCF and LCM from prime factorizations?
GCF: multiply only the shared primes, each at its lower power. LCM: multiply every prime that appears, each at its higher power. For and : GCF = 6 and LCM = 72.
Strategy · 6/8
Word problem: when do you use the GCF and when the LCM?
GCF: splitting things into the largest equal pieces or identical groups (cutting, packing kits). LCM: repeating cycles that must line up again (buses, blinking lights). The GCF is at most the smaller number; the LCM is at least the larger.
Fact · 7/8
What is the sum of three consecutive integers?
Three times the middle one, since n + (n + 1) + (n + 2) = 3n + 3. If the sum is 84, the middle integer is 84 ÷ 3 = 28, so the integers are 27, 28 and 29.
Common trap · 8/8
Is |2 − 10| equal to 12?
No. Simplify inside the bars first: |2 − 10| = |−8| = 8. Absolute value is distance from zero, so it is never negative, and the bars work like grouping symbols.