Highest Common Factor of 612, 936, 458, 370 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 612, 936, 458, 370 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 612, 936, 458, 370 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 612, 936, 458, 370 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 612, 936, 458, 370 is 2.
HCF(612, 936, 458, 370) = 2
HCF of 612, 936, 458, 370 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 612, 936, 458, 370 is 2.
Highest Common Factor of 612,936,458,370 is 2
Step 1: Since 936 > 612, we apply the division lemma to 936 and 612, to get
936 = 612 x 1 + 324
Step 2: Since the reminder 612 ≠ 0, we apply division lemma to 324 and 612, to get
612 = 324 x 1 + 288
Step 3: We consider the new divisor 324 and the new remainder 288, and apply the division lemma to get
324 = 288 x 1 + 36
We consider the new divisor 288 and the new remainder 36, and apply the division lemma to get
288 = 36 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 36, the HCF of 612 and 936 is 36
Notice that 36 = HCF(288,36) = HCF(324,288) = HCF(612,324) = HCF(936,612) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 458 > 36, we apply the division lemma to 458 and 36, to get
458 = 36 x 12 + 26
Step 2: Since the reminder 36 ≠ 0, we apply division lemma to 26 and 36, to get
36 = 26 x 1 + 10
Step 3: We consider the new divisor 26 and the new remainder 10, and apply the division lemma to get
26 = 10 x 2 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 36 and 458 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(26,10) = HCF(36,26) = HCF(458,36) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 370 > 2, we apply the division lemma to 370 and 2, to get
370 = 2 x 185 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 370 is 2
Notice that 2 = HCF(370,2) .
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Frequently Asked Questions on HCF of 612, 936, 458, 370 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 612, 936, 458, 370?
Answer: HCF of 612, 936, 458, 370 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 612, 936, 458, 370 using Euclid's Algorithm?
Answer: For arbitrary numbers 612, 936, 458, 370 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.