Highest Common Factor of 702, 364, 974 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 702, 364, 974 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 702, 364, 974 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 702, 364, 974 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 702, 364, 974 is 2.
HCF(702, 364, 974) = 2
HCF of 702, 364, 974 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 702, 364, 974 is 2.
Highest Common Factor of 702,364,974 is 2
Step 1: Since 702 > 364, we apply the division lemma to 702 and 364, to get
702 = 364 x 1 + 338
Step 2: Since the reminder 364 ≠ 0, we apply division lemma to 338 and 364, to get
364 = 338 x 1 + 26
Step 3: We consider the new divisor 338 and the new remainder 26, and apply the division lemma to get
338 = 26 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 26, the HCF of 702 and 364 is 26
Notice that 26 = HCF(338,26) = HCF(364,338) = HCF(702,364) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 974 > 26, we apply the division lemma to 974 and 26, to get
974 = 26 x 37 + 12
Step 2: Since the reminder 26 ≠ 0, we apply division lemma to 12 and 26, to get
26 = 12 x 2 + 2
Step 3: We consider the new divisor 12 and the new remainder 2, and apply the division lemma to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 26 and 974 is 2
Notice that 2 = HCF(12,2) = HCF(26,12) = HCF(974,26) .
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Frequently Asked Questions on HCF of 702, 364, 974 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 702, 364, 974?
Answer: HCF of 702, 364, 974 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 702, 364, 974 using Euclid's Algorithm?
Answer: For arbitrary numbers 702, 364, 974 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
