Highest Common Factor of 707, 9612, 6984 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 707, 9612, 6984 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 707, 9612, 6984 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 707, 9612, 6984 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 707, 9612, 6984 is 1.
HCF(707, 9612, 6984) = 1
HCF of 707, 9612, 6984 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 707, 9612, 6984 is 1.
Highest Common Factor of 707,9612,6984 is 1
Step 1: Since 9612 > 707, we apply the division lemma to 9612 and 707, to get
9612 = 707 x 13 + 421
Step 2: Since the reminder 707 ≠ 0, we apply division lemma to 421 and 707, to get
707 = 421 x 1 + 286
Step 3: We consider the new divisor 421 and the new remainder 286, and apply the division lemma to get
421 = 286 x 1 + 135
We consider the new divisor 286 and the new remainder 135,and apply the division lemma to get
286 = 135 x 2 + 16
We consider the new divisor 135 and the new remainder 16,and apply the division lemma to get
135 = 16 x 8 + 7
We consider the new divisor 16 and the new remainder 7,and apply the division lemma to get
16 = 7 x 2 + 2
We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get
7 = 2 x 3 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 707 and 9612 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(16,7) = HCF(135,16) = HCF(286,135) = HCF(421,286) = HCF(707,421) = HCF(9612,707) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 6984 > 1, we apply the division lemma to 6984 and 1, to get
6984 = 1 x 6984 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 6984 is 1
Notice that 1 = HCF(6984,1) .
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Frequently Asked Questions on HCF of 707, 9612, 6984 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 707, 9612, 6984?
Answer: HCF of 707, 9612, 6984 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 707, 9612, 6984 using Euclid's Algorithm?
Answer: For arbitrary numbers 707, 9612, 6984 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
