Highest Common Factor of 940, 8205 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 940, 8205 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 940, 8205 is 5 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 940, 8205 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 940, 8205 is 5.
HCF(940, 8205) = 5
HCF of 940, 8205 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 940, 8205 is 5.
Highest Common Factor of 940,8205 is 5
Step 1: Since 8205 > 940, we apply the division lemma to 8205 and 940, to get
8205 = 940 x 8 + 685
Step 2: Since the reminder 940 ≠ 0, we apply division lemma to 685 and 940, to get
940 = 685 x 1 + 255
Step 3: We consider the new divisor 685 and the new remainder 255, and apply the division lemma to get
685 = 255 x 2 + 175
We consider the new divisor 255 and the new remainder 175,and apply the division lemma to get
255 = 175 x 1 + 80
We consider the new divisor 175 and the new remainder 80,and apply the division lemma to get
175 = 80 x 2 + 15
We consider the new divisor 80 and the new remainder 15,and apply the division lemma to get
80 = 15 x 5 + 5
We consider the new divisor 15 and the new remainder 5,and apply the division lemma to get
15 = 5 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 940 and 8205 is 5
Notice that 5 = HCF(15,5) = HCF(80,15) = HCF(175,80) = HCF(255,175) = HCF(685,255) = HCF(940,685) = HCF(8205,940) .
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Frequently Asked Questions on HCF of 940, 8205 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 940, 8205?
Answer: HCF of 940, 8205 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 940, 8205 using Euclid's Algorithm?
Answer: For arbitrary numbers 940, 8205 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.