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Suppose the two digits of the first number are x and y where 0<=x,y<10.
[Strictly speaking, if it is a two digit number then x>0, but the proof still works.]
Then the first number is 10x + y
and the second number, therefore, is 10y + x
Taking the second number away from the first gives: (10x + y) - (10y + x)
= 10x + y - 10y - x = 9x - 9y = 9(x-y)
Now, since x and y are integers, x-y must be an integer.
That is, the result of the subtraction is 9*an integer ie it is a multiple of 9.
What else can I help you with?
Is the factor of the sum of digits equals 9 or a multiple of 9?
If the sum of the digits of a given number equals nine or a multiple of nine, nine is a factor of that number.
When you reverse the digits in a certain two-digit number you increase its value by 9 Find the number if the sum of its digits is 7?
34.
What is the smallest number after 8000 that is divisible by 4 and 9?
By 'after 8000' it looks like 'greater than 8000' is what you want.So to get multiple of 4, last 2 digits must be a multiple of 4. {This is because 100 and every multiple of 100 are multiples of 4, so you only have to look at the last two digits}.For multiple of 9, digits must sum up to 9 (or multiple of 9). So 8001 sums up to 9, but it's not multiple of 4. 8010 doesn't work either. So let's look at digits sum to 18. We already have 8, so the last 2 digits sum to 10 would work, and the last 2 digits multiple of 4:19 : 1+9 = 10, but not multiple of 4.28 : 2+8 = 10, and yes it's a multiple of 4.8028 is the answer.
Is 18324 divisible by 9 and 4?
Yes.A number is divisible by 9 if the sum of the digits is a multiple of 9.18324 = 1 + 8 + 3 + 2 + 4 = 18 (18 is a multiple of 9)A number is divisible by 4 if the last two digits is a multiple of 4.18324 = the last two digits are 24 & it is a multiple of 4.18324 ÷ 9 = 203618324 ÷ 4 = 4581
What is a number pattern in multiples of 9?
The sum of the digits is also a multiple of 9. And, if the sum of the digits is too large, you can sum those digits and keep going.
Dan found a twodigit odd number. one of its digits was half the other. the number was greater than 50. what was it?
63
What is 72 reverse the digits divide by 3?
72 reverse the digits divide by 3 = 24
Is 6618 divisible 3 6 and 9?
Yes, yes, and no. 3- sum of digits must be multiple of 3. 6- sum of digits must be multiple of 3 and number must be even (multiple of 2). 9- sum of digits must be multiple of 9. (The sum of the digits here is 21.)
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
The sum of your two digits is the same as the product of your two digits you are a multiple of 11 who am i?
22
3?
The sum of the digits is a multiple of 3
9?
The sum of the digits is a multiple of 9
Is a number a multiple of 4 of its last two digits are divisible by 4?
Yes If a numbers last two digits (assuming that it has at least two) is a multiple of 4, the whole number is also a multiple of 4. If the last two digits are 00 (assuming in this case it has at least three digits), the number is also a multiple of 4. For example, 100 and 200 are multiples of 4.
What is A multiple of 11 a multiple of 7 the product of its digits is 6?
231
What number is a multiple of 150 factor of 9 has 3 digits and the sum of the digits is 9?
No factor of 9 has three digits. 450 is a three-digit multiple of 150 (and of 9) with a digit sum of 9.
How are the divisibility rules for 3 6 and 9 alike?
A number is divisible by 3 if the sum of its digits is a multiple of 3. A number is divisible by 6 if the sum of its digits is a multiple of 3 and it's even. A number is divisible by 9 if the sum of its digits is a multiple of 9.
The sum of any two-digit number and the number formed by reversing the digits is always divisible by what?
The sum of any two-digit number and the number formed by reversing the digits is always divisible by 11. This is because when you add a two-digit number to its reverse, the result will always be a multiple of 11. This is because the difference between the original number and its reverse is always a multiple of 9, and when you add two multiples of 9, the sum will always be a multiple of 11.
