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What is the formula if the product of the digits is 36 and the number is divisible by...

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joannaguerrero | eNotes Newbie

Posted September 24, 2010 at 8:42 AM via web

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What is the formula if the product of the digits is 36 and the number is divisible by 7.

 

Can't figure out the formula. Need some help on homework for my child please.

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lynn30k | High School Teacher | (Level 3) Associate Educator

Posted September 24, 2010 at 10:22 AM (Answer #1)

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I would think the easiest way to figure out the answer is just to look at multiples of 7, till you get to one where the product of the digits is 36. So....7x1=7. 7x2=14, but 1x4 does not equal 36. 7x3=21...nope.  7x4=28. 7x5=35  7x6=42  7x7=49  Aha!  4x9 does indeed = 36, so 49 would be the solution. I'm not sure how you would go about writing a formula. There doesn't seem to me to be any logical way to do that, because you are talking about two different systems. 

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted September 24, 2010 at 10:45 AM (Answer #2)

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Let the number be ab such tha:

a*b = 36

Then ab coud be :

9*4, 4*9 , 6*6 ,

Then the number could be:

94, 49, or 66

but ab is divisible by 7;

97 and 66 are not divisible by 7.

Then the answer is 49.

Let us check:

the product of the digits = 4*9 = 36    check.

The number is divisible by 7 ==> 49/7 = 7     check.

 

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andrewmezzo | Student, College Freshman | (Level 1) Valedictorian

Posted September 24, 2010 at 9:05 AM (Answer #3)

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What do you mean by formula? The probelm asked you to write a formula for this?

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