Highest Common Factor of 374, 664 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, 664 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 374, 664 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 374, 664 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, 664 is 2.
HCF(374, 664) = 2
HCF of 374, 664 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, 664 is 2.
Highest Common Factor of 374,664 is 2
Step 1: Since 664 > 374, we apply the division lemma to 664 and 374, to get
664 = 374 x 1 + 290
Step 2: Since the reminder 374 ≠ 0, we apply division lemma to 290 and 374, to get
374 = 290 x 1 + 84
Step 3: We consider the new divisor 290 and the new remainder 84, and apply the division lemma to get
290 = 84 x 3 + 38
We consider the new divisor 84 and the new remainder 38,and apply the division lemma to get
84 = 38 x 2 + 8
We consider the new divisor 38 and the new remainder 8,and apply the division lemma to get
38 = 8 x 4 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 374 and 664 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(38,8) = HCF(84,38) = HCF(290,84) = HCF(374,290) = HCF(664,374) .
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Frequently Asked Questions on HCF of 374, 664 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, 664?
Answer: HCF of 374, 664 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 374, 664 using Euclid's Algorithm?
Answer: For arbitrary numbers 374, 664 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.