Divisibility Rules - SSAT Upper Level: Quantitative
Card 1 of 20
Identify whether $7,128$ is divisible by $4$.
Identify whether $7,128$ is divisible by $4$.
Tap to reveal answer
Yes, because the last two digits $28$ are divisible by $4$. Applying the rule for 4, 28 divided by 4 equals 7, an integer, confirming divisibility.
Yes, because the last two digits $28$ are divisible by $4$. Applying the rule for 4, 28 divided by 4 equals 7, an integer, confirming divisibility.
← Didn't Know|Knew It →
Identify whether $5,376$ is divisible by $8$.
Identify whether $5,376$ is divisible by $8$.
Tap to reveal answer
Yes, because the last three digits $376$ are divisible by $8$. Applying the rule for 8, 376 divided by 8 equals 47, an integer, confirming divisibility.
Yes, because the last three digits $376$ are divisible by $8$. Applying the rule for 8, 376 divided by 8 equals 47, an integer, confirming divisibility.
← Didn't Know|Knew It →
Identify whether $93,615$ is divisible by $5$.
Identify whether $93,615$ is divisible by $5$.
Tap to reveal answer
Yes, because the last digit is $5$. The rule for 5 is satisfied as the number ends in 5, making it divisible by 5.
Yes, because the last digit is $5$. The rule for 5 is satisfied as the number ends in 5, making it divisible by 5.
← Didn't Know|Knew It →
Identify whether $4,572$ is divisible by $3$.
Identify whether $4,572$ is divisible by $3$.
Tap to reveal answer
Yes, because $4+5+7+2=18$ and $18$ is divisible by $3$. The sum 18 is divisible by 3 since $18 \div 3 = 6$, applying the rule for 3.
Yes, because $4+5+7+2=18$ and $18$ is divisible by $3$. The sum 18 is divisible by 3 since $18 \div 3 = 6$, applying the rule for 3.
← Didn't Know|Knew It →
Identify whether $2,418$ is divisible by $6$.
Identify whether $2,418$ is divisible by $6$.
Tap to reveal answer
Yes, it is divisible by $2$ and $3$. It satisfies the rules for both 2 (even) and 3 (sum 15 divisible by 3), hence divisible by 6.
Yes, it is divisible by $2$ and $3$. It satisfies the rules for both 2 (even) and 3 (sum 15 divisible by 3), hence divisible by 6.
← Didn't Know|Knew It →
Identify whether $13,530$ is divisible by $10$.
Identify whether $13,530$ is divisible by $10$.
Tap to reveal answer
Yes, because the last digit is $0$. The rule for 10 is met as the number ends in 0, confirming divisibility.
Yes, because the last digit is $0$. The rule for 10 is met as the number ends in 0, confirming divisibility.
← Didn't Know|Knew It →
Identify whether $73,205$ is divisible by $2$.
Identify whether $73,205$ is divisible by $2$.
Tap to reveal answer
No, because the last digit $5$ is odd. The units digit 5 is odd, so the number is not even and thus not divisible by 2.
No, because the last digit $5$ is odd. The units digit 5 is odd, so the number is not even and thus not divisible by 2.
← Didn't Know|Knew It →
Identify whether $47,190$ is divisible by $9$.
Identify whether $47,190$ is divisible by $9$.
Tap to reveal answer
No, because $4+7+1+9+0=21$ and $21$ is not divisible by $9$. The sum 21 is not divisible by 9 (between 18 and 27), so the number is not divisible by 9.
No, because $4+7+1+9+0=21$ and $21$ is not divisible by $9$. The sum 21 is not divisible by 9 (between 18 and 27), so the number is not divisible by 9.
← Didn't Know|Knew It →
Identify whether $10^5+10^3$ is divisible by $10$.
Identify whether $10^5+10^3$ is divisible by $10$.
Tap to reveal answer
Yes, $10^5+10^3=101000$ ends in $0$. The expression simplifies to 101000, which ends in 0, satisfying the rule for 10.
Yes, $10^5+10^3=101000$ ends in $0$. The expression simplifies to 101000, which ends in 0, satisfying the rule for 10.
← Didn't Know|Knew It →
Identify whether $10^6-1$ is divisible by $9$.
Identify whether $10^6-1$ is divisible by $9$.
Tap to reveal answer
Yes, $10^6-1=999999$ and $9+9+9+9+9+9=54$ is divisible by $9$. The sum of digits 54 is divisible by 9 ($54 \div 9 = 6$), confirming divisibility.
Yes, $10^6-1=999999$ and $9+9+9+9+9+9=54$ is divisible by $9$. The sum of digits 54 is divisible by 9 ($54 \div 9 = 6$), confirming divisibility.
← Didn't Know|Knew It →
Identify whether $10^4+10^2+1$ is divisible by $3$.
Identify whether $10^4+10^2+1$ is divisible by $3$.
Tap to reveal answer
Yes, $10^4+10^2+1=10101$ and $1+0+1+0+1=3$. The sum of digits is 3, which is divisible by 3 ($3 \div 3 = 1$), confirming divisibility.
Yes, $10^4+10^2+1=10101$ and $1+0+1+0+1=3$. The sum of digits is 3, which is divisible by 3 ($3 \div 3 = 1$), confirming divisibility.
← Didn't Know|Knew It →
What is the remainder when $10^7$ is divided by $9$?
What is the remainder when $10^7$ is divided by $9$?
Tap to reveal answer
$1$. Since $10 \equiv 1 \pmod{9}$, $10^7 \equiv 1 \pmod{9}$, yielding remainder 1.
$1$. Since $10 \equiv 1 \pmod{9}$, $10^7 \equiv 1 \pmod{9}$, yielding remainder 1.
← Didn't Know|Knew It →
What is the remainder when $10^5+7$ is divided by $3$?
What is the remainder when $10^5+7$ is divided by $3$?
Tap to reveal answer
$2$. Since $10 \equiv 1 \pmod{3}$, $10^5 +7 \equiv 1+7=8 \equiv 2 \pmod{3}$.
$2$. Since $10 \equiv 1 \pmod{3}$, $10^5 +7 \equiv 1+7=8 \equiv 2 \pmod{3}$.
← Didn't Know|Knew It →
State the divisibility rule for $2$.
State the divisibility rule for $2$.
Tap to reveal answer
Divisible by $2$ iff the last digit is even ($0,2,4,6,8$). A number is divisible by 2 if it is even, which is determined solely by the parity of its units digit.
Divisible by $2$ iff the last digit is even ($0,2,4,6,8$). A number is divisible by 2 if it is even, which is determined solely by the parity of its units digit.
← Didn't Know|Knew It →
State the divisibility rule for $3$.
State the divisibility rule for $3$.
Tap to reveal answer
Divisible by $3$ iff the sum of digits is divisible by $3$. Since $10 \equiv 1 \pmod{3}$, a number is congruent to the sum of its digits modulo 3.
Divisible by $3$ iff the sum of digits is divisible by $3$. Since $10 \equiv 1 \pmod{3}$, a number is congruent to the sum of its digits modulo 3.
← Didn't Know|Knew It →
State the divisibility rule for $4$.
State the divisibility rule for $4$.
Tap to reveal answer
Divisible by $4$ iff the last two digits form a multiple of $4$. Since $100 \equiv 0 \pmod{4}$, divisibility by 4 depends only on the last two digits forming a multiple of 4.
Divisible by $4$ iff the last two digits form a multiple of $4$. Since $100 \equiv 0 \pmod{4}$, divisibility by 4 depends only on the last two digits forming a multiple of 4.
← Didn't Know|Knew It →
State the divisibility rule for $5$.
State the divisibility rule for $5$.
Tap to reveal answer
Divisible by $5$ iff the last digit is $0$ or $5$. Since $10 \equiv 0 \pmod{5}$, the number is divisible by 5 precisely when its units digit is 0 or 5.
Divisible by $5$ iff the last digit is $0$ or $5$. Since $10 \equiv 0 \pmod{5}$, the number is divisible by 5 precisely when its units digit is 0 or 5.
← Didn't Know|Knew It →
State the divisibility rule for $8$.
State the divisibility rule for $8$.
Tap to reveal answer
Divisible by $8$ iff the last three digits form a multiple of $8$. Since $1000 \equiv 0 \pmod{8}$, divisibility by 8 is determined by the last three digits being a multiple of 8.
Divisible by $8$ iff the last three digits form a multiple of $8$. Since $1000 \equiv 0 \pmod{8}$, divisibility by 8 is determined by the last three digits being a multiple of 8.
← Didn't Know|Knew It →
State the divisibility rule for $9$.
State the divisibility rule for $9$.
Tap to reveal answer
Divisible by $9$ iff the sum of digits is divisible by $9$. Since $10 \equiv 1 \pmod{9}$, a number is congruent to the sum of its digits modulo 9.
Divisible by $9$ iff the sum of digits is divisible by $9$. Since $10 \equiv 1 \pmod{9}$, a number is congruent to the sum of its digits modulo 9.
← Didn't Know|Knew It →
State the divisibility rule for $11$ using alternating digit sums.
State the divisibility rule for $11$ using alternating digit sums.
Tap to reveal answer
Divisible by $11$ iff the alternating sum of digits is a multiple of $11$. Since $10 \equiv -1 \pmod{11}$, the alternating sum of digits determines congruence modulo 11.
Divisible by $11$ iff the alternating sum of digits is a multiple of $11$. Since $10 \equiv -1 \pmod{11}$, the alternating sum of digits determines congruence modulo 11.
← Didn't Know|Knew It →