Highest Common Factor of 688, 948, 412 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, 948, 412 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 688, 948, 412 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, 948, 412 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, 948, 412 is 4.
HCF(688, 948, 412) = 4
HCF of 688, 948, 412 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, 948, 412 is 4.
Highest Common Factor of 688,948,412 is 4
Step 1: Since 948 > 688, we apply the division lemma to 948 and 688, to get
948 = 688 x 1 + 260
Step 2: Since the reminder 688 ≠ 0, we apply division lemma to 260 and 688, to get
688 = 260 x 2 + 168
Step 3: We consider the new divisor 260 and the new remainder 168, and apply the division lemma to get
260 = 168 x 1 + 92
We consider the new divisor 168 and the new remainder 92,and apply the division lemma to get
168 = 92 x 1 + 76
We consider the new divisor 92 and the new remainder 76,and apply the division lemma to get
92 = 76 x 1 + 16
We consider the new divisor 76 and the new remainder 16,and apply the division lemma to get
76 = 16 x 4 + 12
We consider the new divisor 16 and the new remainder 12,and apply the division lemma to get
16 = 12 x 1 + 4
We consider the new divisor 12 and the new remainder 4,and apply the division lemma to get
12 = 4 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 688 and 948 is 4
Notice that 4 = HCF(12,4) = HCF(16,12) = HCF(76,16) = HCF(92,76) = HCF(168,92) = HCF(260,168) = HCF(688,260) = HCF(948,688) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 412 > 4, we apply the division lemma to 412 and 4, to get
412 = 4 x 103 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 4 and 412 is 4
Notice that 4 = HCF(412,4) .
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Frequently Asked Questions on HCF of 688, 948, 412 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, 948, 412?
Answer: HCF of 688, 948, 412 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 688, 948, 412 using Euclid's Algorithm?
Answer: For arbitrary numbers 688, 948, 412 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.