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What five digits appear as the last digit of the multiples of 2?
0,2,4,6,8
What pattern do you see in the multiples of 8?
The units digits start with 8 and go down in steps of 2. The units digit repeats every 5 multiples, The last pair of digits repeat every 25 multiples.
What digits are in the ones place of the numbers that have 5 as one of their factors?
The "ones" place is always the last digit in any number so multiples of 5 always have either 5 or 0 (zero) in the "ones" digit position.
How does the divisibility rule for 4 and 8 work?
A number is a multiple of 4 if the last 2 digits are a multiple of 4 The 10s digit is even and the last digit is 0, 4 or 8 The 10s digit is odd and the last digit is 2 or 6 A number is a multiple of 8 if the last 3 digits are a multiple of 8 The 100s digit is even and the last 2 digits are a multiple of 8 The 100s digit is odd and the last 2 digits are 4 times an odd number
How do you find estimated digits in a number?
The last digit is always the estimated digit in a number
What five digits appear as the last digit of the multiples of 2?
0,2,4,6,8
What pattern do you see in the multiples of 8?
The units digits start with 8 and go down in steps of 2. The units digit repeats every 5 multiples, The last pair of digits repeat every 25 multiples.
What five numbers appear as the last digit of the multiples of 4?
0, 2, 4, 6, 8
The divisibility rules of the 1st 10 powers of 2?
2: The number ends in 0, 2, 4, 6 or 8 4 : The last 2 digits are a multiple of 4 The 10s digit is even and the last digit is 0, 4 or 8 The 10s digit is odd and the last digit is 2 or 6 8: The last 3 digits are a multiple of 8 The 100s digit is even and the last 2 digits are a multiple of 8 The 100s digit is odd and the last 2 digits are 4 times an odd number 16: The last 4 digits are a multiple of 16 The 1,000s digit is even and the last 3 digits are a multiple of 16 The 1,000s digit is odd and the last 3 digits are 8 times an odd number 32: The last 5 digits are a multiple of 32 The 10,000s digit is even and the last 4 digits are a multiple of 32 The 10,000s digit is odd and the last 4 digits are 16 times an odd number 64: The last 6 digits are a multiple of 64 The 100,000s digit is even and the last 5 digits are a multiple of 64 The 100,000s digit is odd and the last 5 digits are 32 times an odd number 128: The last 7 digits are a multiple of 128 The 1,000,000s digit is even and the last 6 digits are a multiple of 128 The 1,000,000s digit is odd and the last 6 digits are 64 times an odd number 256: The last 8 digits are a multiple of 256 The 10,000,000s digit is even and the last 7 digits are a multiple of 256 The 10,000,000s digit is odd and the last 7 digits are 128 times an odd number 512: The last 9 digits are a multiple of 512 The 100,000,000s digit is even and the last 8 digits are a multiple of 512 The 100,000,000s digit is odd and the last 8 digits are 256 times an odd number 1,024: The last 10 digits are a multiple of 1,024 The 1,000,000,000s digit is even and the last 9 digits are a multiple of 1,024 The 1,000,000,000s digit is odd and the last 9 digits are 512 times an odd number
What is the penultimate digit of factorial 99?
To find the penultimate digit of 99!, we first note that 99! has many factors of 10 due to the number of multiples of 5 and 2 present in the product. Specifically, there are 24 trailing zeros in 99!, which means the last two digits are 00. Therefore, the penultimate digit of 99! is 9, as the last two digits are 00.
40?
The last 3 digits are a multiple of 40The 100s digit is even and the last 2 digits are 00, 40 or 80The 100s digit is odd and the last 2 digits are 20 or 60
How many 3 digit counting numbers are not multiples of 5?
There are 720 of them. The three digit counting numbers are 100-999. All multiples of 5 have their last digit as 0 or 5. There are 9 possible numbers {1-9} for the first digit, There are 10 possible numbers {0-9} for each of the first digits, There are 8 possible numbers {1-4, 6-9} for each of the first two digits, Making 9 x 10 x 8 = 720 possible 3 digit counting numbers not multiples of 5.
What is the last digit of 21999x32000?
To find the last digit of ( 21999 \times 32000 ), we can focus on the last digits of the numbers involved. The last digit of ( 21999 ) is ( 9 ) and the last digit of ( 32000 ) is ( 0 ). Multiplying these last digits gives ( 9 \times 0 = 0 ). Therefore, the last digit of ( 21999 \times 32000 ) is ( 0 ).
8?
The last 3 digits are a multiple of 8:The 100s digit is even and the last 2 digits are a multiple of 8The 100s digit is odd and the last 2 digits are 4 times an odd number
32?
The last 5 digits are a multiple of 32The 10,000s digit is even and the last 4 digits are a multiple of 32The 10,000s digit is odd and the last 4 digits are 16 times an odd number
80?
The last 4 digits are a multiple of 80The 1,000s digit is even and the last 3 digits are a multiple of 80The 1,000s digit is odd and the last 3 digits are 40 times an odd number
The divisibility rules of the 1st 10 powers of 5?
5: The number ends in 0 or 5 25: The number ends in 00, 25, 50 or 75 125: The number ends in 000, 125, 250, 375, 500, 625, 750 or 875 625: The last 4 digits are a multiple of 625 The 1,000s digit is 0 or 5 and the last 3 digits are 000 or 625 The 1,000s digit is 1 or 6 and the last 3 digits are 250 or 875 The 1,000s digit is 2 or 7 and the last 3 digits are 500 The 1,000s digit is 3 or 8 and the last 3 digits are 125 or 750 The 1,000s digit is 4 or 9 and the last 3 digits are 375 3,125: The last 5 digits are a multiple of 3,125 The 10,000s digit is 0 or 5 and the last 4 digits are a multiple of 3,125 The 10,000s digit is 1 or 6 and the last 4 digits are 625 times a number that ends in 4 or 9 The 10,000s digit is 2 or 7 and the last 4 digits are 625 times a number that ends in 3 or 8 The 10,000s digit is 3 or 8 and the last 4 digits are 625 times a number that ends in 2 or 7 The 10,000s digit is 4 or 9 and the last 4 digits are 625 times a number that ends in 1 or 6 15,625: The last 6 digits are a multiple of 15,625 The 100,000s digit is 0 or 5 and the last 5 digits are a multiple of 15,625 The 100,000s digit is 1 or 6 and the last 5 digits are 3,125 times a number that ends in 3 or 8 The 100,000s digit is 2 or 7 and the last 5 digits are 3,125 times a number that ends in 1 or 6 The 100,000s digit is 3 or 8 and the last 5 digits are 3,125 times a number that ends in 4 or 9 The 100,000s digit is 4 or 9 and the last 5 digits are 3,125 times a number that ends in 2 or 7 78,125: The last 7 digits are a multiple of 78,125 The 1,000,000s digit is 0 or 5 and the last 6 digits are a multiple of 78,125 The 1,000,000s digit is 1 or 6 and the last 6 digits are 15,625 times a number that ends in 1 or 6 The 1,000,000s digit is 2 or 7 and the last 6 digits are 15,625 times a number that ends in 2 or 7 The 1,000,000s digit is 3 or 8 and the last 6 digits are 15,625 times a number that ends in 3 or 8 The 1,000,000s digit is 4 or 9 and the last 6 digits are 15,625 times a number that ends in 4 or 9 390,625: The last 8 digits are a multiple of 390,625 The 10,000,000s digit is 0 or 5 and the last 7 digits are a multiple of 390,625 The 10,000,000s digit is 1 or 6 and the last 7 digits are 78,125 times a number that ends in 2 or 7 The 10,000,000s digit is 2 or 7 and the last 7 digits are 78,125 times a number that ends in 4 or 9 The 10,000,000s digit is 3 or 8 and the last 7 digits are 78,125 times a number that ends in 1 or 6 The 10,000,000s digit is 4 or 9 and the last 7 digits are 78,125 rimes a number that ends in 3 or 8 1,953,125: The last 9 digits are a multiple of 1,953,125 The 100,000,000s digit is 0 or 5 and the last 8 digits are a multiple of 1,953,125 The 100,000,000s digit is 1 or 6 and the last 8 digits are 390,625 times a number that ends in 4 or 9 The 100,000,000s digit is 2 or 7 and the last 8 digits are 390,625 times a number that ends in 3 or 8 The 100,000,000s digit is 3 or 8 and the last 8 digits are 390,625 times a number that ends in 2 or 7 The 100,000,000s digit is 4 or 9 and the last 8 digits are 390,625 times a number that ends in 1 or 6 9,765,625: The last 10 digits are a multiple of 9,765,625 The 1,000,000,000s digit is 0 or 5 and the last 9 digits are a multiple of 9,765,625 The 1,000,000,000s digit is 1 or 6 and the last 9 digits are 1,953,125 times a number that ends in 3 or 8 The 1,000,000,000s digit is 2 or 7 and the last 9 digits are 1,953,125 times a number that ends in 1 or 6 The 1,000,000,000s digit is 3 or 8 and the last 9 digits are 1,953,125 times a number that ends in 4 or 9 The 1,000,000,000s digit is 4 or 9 and the last 9 digits are 1,953,125 times a number that ends in 2 or 7
