Find the greatest number that divides 85 and 140 exactly
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Find the greatest number that divides 85 and 140 exactly
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The required number is 5.
Step-by-step explanation:
Each time when the number divides 143, 67 and 89 it leaves remainder 3, 7 and 4 respectively.
So, the number exactly divides (143 - 3), (67 - 7) and (89 - 4) ⇒ the number divides 140, 60 and 85
So, the required number which when divides 143, 67 and 89 and leaves remainder 3, 7 and 4 respectively will be HCF (140, 60, 85)
Now, to find HCF (140, 60, 85) : Find the prime factors of 140, 60 and 85
140 = 2 × 2 × 5 × 7
60 = 2 × 2 × 3 × 5
85 = 5 × 17
So, we can see the common factor in all the numbers is 5
⇒ HCF = 5
So, the greatest number which when divides 143, 67 and 89 leaves remainder 3, 7 and 4 respectively will be 5