Highest Common Factor of 661, 8352 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 661, 8352 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 661, 8352 is 1 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 661, 8352 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 661, 8352 is 1.
HCF(661, 8352) = 1
HCF of 661, 8352 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 661, 8352 is 1.
Highest Common Factor of 661,8352 is 1
Step 1: Since 8352 > 661, we apply the division lemma to 8352 and 661, to get
8352 = 661 x 12 + 420
Step 2: Since the reminder 661 ≠ 0, we apply division lemma to 420 and 661, to get
661 = 420 x 1 + 241
Step 3: We consider the new divisor 420 and the new remainder 241, and apply the division lemma to get
420 = 241 x 1 + 179
We consider the new divisor 241 and the new remainder 179,and apply the division lemma to get
241 = 179 x 1 + 62
We consider the new divisor 179 and the new remainder 62,and apply the division lemma to get
179 = 62 x 2 + 55
We consider the new divisor 62 and the new remainder 55,and apply the division lemma to get
62 = 55 x 1 + 7
We consider the new divisor 55 and the new remainder 7,and apply the division lemma to get
55 = 7 x 7 + 6
We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get
7 = 6 x 1 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 661 and 8352 is 1
Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(55,7) = HCF(62,55) = HCF(179,62) = HCF(241,179) = HCF(420,241) = HCF(661,420) = HCF(8352,661) .
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Frequently Asked Questions on HCF of 661, 8352 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 661, 8352?
Answer: HCF of 661, 8352 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 661, 8352 using Euclid's Algorithm?
Answer: For arbitrary numbers 661, 8352 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.