Highest Common Factor of 688, 7940, 4156 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 688, 7940, 4156 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 688, 7940, 4156 is 4 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 688, 7940, 4156 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 688, 7940, 4156 is 4.
HCF(688, 7940, 4156) = 4
HCF of 688, 7940, 4156 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 688, 7940, 4156 is 4.
Highest Common Factor of 688,7940,4156 is 4
Step 1: Since 7940 > 688, we apply the division lemma to 7940 and 688, to get
7940 = 688 x 11 + 372
Step 2: Since the reminder 688 ≠ 0, we apply division lemma to 372 and 688, to get
688 = 372 x 1 + 316
Step 3: We consider the new divisor 372 and the new remainder 316, and apply the division lemma to get
372 = 316 x 1 + 56
We consider the new divisor 316 and the new remainder 56,and apply the division lemma to get
316 = 56 x 5 + 36
We consider the new divisor 56 and the new remainder 36,and apply the division lemma to get
56 = 36 x 1 + 20
We consider the new divisor 36 and the new remainder 20,and apply the division lemma to get
36 = 20 x 1 + 16
We consider the new divisor 20 and the new remainder 16,and apply the division lemma to get
20 = 16 x 1 + 4
We consider the new divisor 16 and the new remainder 4,and apply the division lemma to get
16 = 4 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 688 and 7940 is 4
Notice that 4 = HCF(16,4) = HCF(20,16) = HCF(36,20) = HCF(56,36) = HCF(316,56) = HCF(372,316) = HCF(688,372) = HCF(7940,688) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 4156 > 4, we apply the division lemma to 4156 and 4, to get
4156 = 4 x 1039 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 4 and 4156 is 4
Notice that 4 = HCF(4156,4) .
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Frequently Asked Questions on HCF of 688, 7940, 4156 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 688, 7940, 4156?
Answer: HCF of 688, 7940, 4156 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 688, 7940, 4156 using Euclid's Algorithm?
Answer: For arbitrary numbers 688, 7940, 4156 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.