Highest Common Factor of 608, 380, 446 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 608, 380, 446 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 608, 380, 446 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 608, 380, 446 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 608, 380, 446 is 2.
HCF(608, 380, 446) = 2
HCF of 608, 380, 446 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 608, 380, 446 is 2.
Highest Common Factor of 608,380,446 is 2
Step 1: Since 608 > 380, we apply the division lemma to 608 and 380, to get
608 = 380 x 1 + 228
Step 2: Since the reminder 380 ≠ 0, we apply division lemma to 228 and 380, to get
380 = 228 x 1 + 152
Step 3: We consider the new divisor 228 and the new remainder 152, and apply the division lemma to get
228 = 152 x 1 + 76
We consider the new divisor 152 and the new remainder 76, and apply the division lemma to get
152 = 76 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 76, the HCF of 608 and 380 is 76
Notice that 76 = HCF(152,76) = HCF(228,152) = HCF(380,228) = HCF(608,380) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 446 > 76, we apply the division lemma to 446 and 76, to get
446 = 76 x 5 + 66
Step 2: Since the reminder 76 ≠ 0, we apply division lemma to 66 and 76, to get
76 = 66 x 1 + 10
Step 3: We consider the new divisor 66 and the new remainder 10, and apply the division lemma to get
66 = 10 x 6 + 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 76 and 446 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(66,10) = HCF(76,66) = HCF(446,76) .
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Frequently Asked Questions on HCF of 608, 380, 446 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 608, 380, 446?
Answer: HCF of 608, 380, 446 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 608, 380, 446 using Euclid's Algorithm?
Answer: For arbitrary numbers 608, 380, 446 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.