Highest Common Factor of 760, 7038 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 760, 7038 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 760, 7038 is 2 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 760, 7038 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 760, 7038 is 2.
HCF(760, 7038) = 2
HCF of 760, 7038 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 760, 7038 is 2.
Highest Common Factor of 760,7038 is 2
Step 1: Since 7038 > 760, we apply the division lemma to 7038 and 760, to get
7038 = 760 x 9 + 198
Step 2: Since the reminder 760 ≠ 0, we apply division lemma to 198 and 760, to get
760 = 198 x 3 + 166
Step 3: We consider the new divisor 198 and the new remainder 166, and apply the division lemma to get
198 = 166 x 1 + 32
We consider the new divisor 166 and the new remainder 32,and apply the division lemma to get
166 = 32 x 5 + 6
We consider the new divisor 32 and the new remainder 6,and apply the division lemma to get
32 = 6 x 5 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 760 and 7038 is 2
Notice that 2 = HCF(6,2) = HCF(32,6) = HCF(166,32) = HCF(198,166) = HCF(760,198) = HCF(7038,760) .
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Frequently Asked Questions on HCF of 760, 7038 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 760, 7038?
Answer: HCF of 760, 7038 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 760, 7038 using Euclid's Algorithm?
Answer: For arbitrary numbers 760, 7038 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.