Highest Common Factor of 904, 6997 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 904, 6997 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 904, 6997 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 904, 6997 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 904, 6997 is 1.
HCF(904, 6997) = 1
HCF of 904, 6997 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 904, 6997 is 1.
Highest Common Factor of 904,6997 is 1
Step 1: Since 6997 > 904, we apply the division lemma to 6997 and 904, to get
6997 = 904 x 7 + 669
Step 2: Since the reminder 904 ≠ 0, we apply division lemma to 669 and 904, to get
904 = 669 x 1 + 235
Step 3: We consider the new divisor 669 and the new remainder 235, and apply the division lemma to get
669 = 235 x 2 + 199
We consider the new divisor 235 and the new remainder 199,and apply the division lemma to get
235 = 199 x 1 + 36
We consider the new divisor 199 and the new remainder 36,and apply the division lemma to get
199 = 36 x 5 + 19
We consider the new divisor 36 and the new remainder 19,and apply the division lemma to get
36 = 19 x 1 + 17
We consider the new divisor 19 and the new remainder 17,and apply the division lemma to get
19 = 17 x 1 + 2
We consider the new divisor 17 and the new remainder 2,and apply the division lemma to get
17 = 2 x 8 + 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 904 and 6997 is 1
Notice that 1 = HCF(2,1) = HCF(17,2) = HCF(19,17) = HCF(36,19) = HCF(199,36) = HCF(235,199) = HCF(669,235) = HCF(904,669) = HCF(6997,904) .
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Frequently Asked Questions on HCF of 904, 6997 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 904, 6997?
Answer: HCF of 904, 6997 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 904, 6997 using Euclid's Algorithm?
Answer: For arbitrary numbers 904, 6997 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.