Highest Common Factor of 670, 402, 774 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 670, 402, 774 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 670, 402, 774 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 670, 402, 774 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 670, 402, 774 is 2.
HCF(670, 402, 774) = 2
HCF of 670, 402, 774 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 670, 402, 774 is 2.
Highest Common Factor of 670,402,774 is 2
Step 1: Since 670 > 402, we apply the division lemma to 670 and 402, to get
670 = 402 x 1 + 268
Step 2: Since the reminder 402 ≠ 0, we apply division lemma to 268 and 402, to get
402 = 268 x 1 + 134
Step 3: We consider the new divisor 268 and the new remainder 134, and apply the division lemma to get
268 = 134 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 134, the HCF of 670 and 402 is 134
Notice that 134 = HCF(268,134) = HCF(402,268) = HCF(670,402) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 774 > 134, we apply the division lemma to 774 and 134, to get
774 = 134 x 5 + 104
Step 2: Since the reminder 134 ≠ 0, we apply division lemma to 104 and 134, to get
134 = 104 x 1 + 30
Step 3: We consider the new divisor 104 and the new remainder 30, and apply the division lemma to get
104 = 30 x 3 + 14
We consider the new divisor 30 and the new remainder 14,and apply the division lemma to get
30 = 14 x 2 + 2
We consider the new divisor 14 and the new remainder 2,and apply the division lemma to get
14 = 2 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 134 and 774 is 2
Notice that 2 = HCF(14,2) = HCF(30,14) = HCF(104,30) = HCF(134,104) = HCF(774,134) .
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Frequently Asked Questions on HCF of 670, 402, 774 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 670, 402, 774?
Answer: HCF of 670, 402, 774 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 670, 402, 774 using Euclid's Algorithm?
Answer: For arbitrary numbers 670, 402, 774 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.