Is 72,424 is divisible by which of the following numbers: 2, 3, 4, 5, 6, 7, 8, 9, or 10. Show and/or explain how you find your answer(s). (2 points)
To check if 72,424 is divisible by a certain number, we need to see if it gives a remainder of 0 when divided by that number.
1) 72,424 ÷ 2 = 36,212 remainder 0 --> Yes, 72,424 is divisible by 2.
2) 72,424 ÷ 3 = 24,141 remainder 1 --> No, 72,424 is not divisible by 3.
3) 72,424 ÷ 4 = 18,106 remainder 0 --> Yes, 72,424 is divisible by 4.
4) 72,424 ÷ 5 = 14,484 remainder 4 --> No, 72,424 is not divisible by 5.
5) 72,424 ÷ 6 = 12,070 remainder 4 --> No, 72,424 is not divisible by 6.
6) 72,424 ÷ 7 = 10,346 remainder 2 --> No, 72,424 is not divisible by 7.
7) 72,424 ÷ 8 = 9,053 remainder 0 --> Yes, 72,424 is divisible by 8.
8) 72,424 ÷ 9 = 8,047 remainder 7 --> No, 72,424 is not divisible by 9.
9) 72,424 ÷ 10 = 7,242 remainder 4 --> No, 72,424 is not divisible by 10.
Therefore, 72,424 is divisible by 2, 4, and 8.
To find out if a number is divisible by another number, we need to check if the first number is a multiple of the second number. Here's how we can determine if 72,424 is divisible by each of the numbers listed:
1. Divisible by 2: A number is divisible by 2 if its last digit is even. Since the last digit of 72,424 is 4 (an even number), it is divisible by 2.
2. Divisible by 3: To test if a number is divisible by 3, we can add up all its digits and check if the sum is divisible by 3. The sum of the digits of 72,424 is 7 + 2 + 4 + 2 + 4 = 19. Since 19 is not divisible by 3, 72,424 is not divisible by 3.
3. Divisible by 4: A number is divisible by 4 if its last two digits form a number divisible by 4. The last two digits of 72,424 are 24, which is divisible by 4. Therefore, 72,424 is divisible by 4.
4. Divisible by 5: A number is divisible by 5 if its last digit is either 0 or 5. Since the last digit of 72,424 is 4 (not divisible by 5), it is not divisible by 5.
5. Divisible by 6: A number is divisible by 6 if it is divisible by both 2 and 3. We already established that 72,424 is divisible by 2, but not by 3. Therefore, it is not divisible by 6.
6. Divisible by 7: There is no simple divisibility rule for 7, so we need to perform long division. 72,424 ÷ 7 = 10,346 remainder 2. Since there is a remainder of 2, 72,424 is not divisible by 7.
7. Divisible by 8: A number is divisible by 8 if its last three digits form a number divisible by 8. The last three digits of 72,424 are 424, which is divisible by 8. Therefore, 72,424 is divisible by 8.
8. Divisible by 9: A number is divisible by 9 if the sum of its digits is divisible by 9. As mentioned earlier, the sum of the digits of 72,424 is 19, which is not divisible by 9. Therefore, 72,424 is not divisible by 9.
9. Divisible by 10: A number is divisible by 10 if its last digit is 0. Since the last digit of 72,424 is 4 (not 0), it is not divisible by 10.
Based on the above analysis, 72,424 is divisible by 2, 4, and 8.