Highest Common Factor of 974, 614, 146 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 974, 614, 146 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 974, 614, 146 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 974, 614, 146 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 974, 614, 146 is 2.
HCF(974, 614, 146) = 2
HCF of 974, 614, 146 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 974, 614, 146 is 2.
Highest Common Factor of 974,614,146 is 2
Step 1: Since 974 > 614, we apply the division lemma to 974 and 614, to get
974 = 614 x 1 + 360
Step 2: Since the reminder 614 ≠ 0, we apply division lemma to 360 and 614, to get
614 = 360 x 1 + 254
Step 3: We consider the new divisor 360 and the new remainder 254, and apply the division lemma to get
360 = 254 x 1 + 106
We consider the new divisor 254 and the new remainder 106,and apply the division lemma to get
254 = 106 x 2 + 42
We consider the new divisor 106 and the new remainder 42,and apply the division lemma to get
106 = 42 x 2 + 22
We consider the new divisor 42 and the new remainder 22,and apply the division lemma to get
42 = 22 x 1 + 20
We consider the new divisor 22 and the new remainder 20,and apply the division lemma to get
22 = 20 x 1 + 2
We consider the new divisor 20 and the new remainder 2,and apply the division lemma to get
20 = 2 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 974 and 614 is 2
Notice that 2 = HCF(20,2) = HCF(22,20) = HCF(42,22) = HCF(106,42) = HCF(254,106) = HCF(360,254) = HCF(614,360) = HCF(974,614) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 146 > 2, we apply the division lemma to 146 and 2, to get
146 = 2 x 73 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 146 is 2
Notice that 2 = HCF(146,2) .
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Frequently Asked Questions on HCF of 974, 614, 146 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 974, 614, 146?
Answer: HCF of 974, 614, 146 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 974, 614, 146 using Euclid's Algorithm?
Answer: For arbitrary numbers 974, 614, 146 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.