Highest Common Factor of 374, 696, 15, 674 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 374, 696, 15, 674 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 374, 696, 15, 674 is 1 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 374, 696, 15, 674 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 374, 696, 15, 674 is 1.
HCF(374, 696, 15, 674) = 1
HCF of 374, 696, 15, 674 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 374, 696, 15, 674 is 1.
Highest Common Factor of 374,696,15,674 is 1
Step 1: Since 696 > 374, we apply the division lemma to 696 and 374, to get
696 = 374 x 1 + 322
Step 2: Since the reminder 374 ≠ 0, we apply division lemma to 322 and 374, to get
374 = 322 x 1 + 52
Step 3: We consider the new divisor 322 and the new remainder 52, and apply the division lemma to get
322 = 52 x 6 + 10
We consider the new divisor 52 and the new remainder 10,and apply the division lemma to get
52 = 10 x 5 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 374 and 696 is 2
Notice that 2 = HCF(10,2) = HCF(52,10) = HCF(322,52) = HCF(374,322) = HCF(696,374) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 15 > 2, we apply the division lemma to 15 and 2, to get
15 = 2 x 7 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 15 is 1
Notice that 1 = HCF(2,1) = HCF(15,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 674 > 1, we apply the division lemma to 674 and 1, to get
674 = 1 x 674 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 674 is 1
Notice that 1 = HCF(674,1) .
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Frequently Asked Questions on HCF of 374, 696, 15, 674 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 374, 696, 15, 674?
Answer: HCF of 374, 696, 15, 674 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 374, 696, 15, 674 using Euclid's Algorithm?
Answer: For arbitrary numbers 374, 696, 15, 674 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.