Highest Common Factor of 780, 598, 354 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 780, 598, 354 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 780, 598, 354 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 780, 598, 354 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 780, 598, 354 is 2.
HCF(780, 598, 354) = 2
HCF of 780, 598, 354 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 780, 598, 354 is 2.
Highest Common Factor of 780,598,354 is 2
Step 1: Since 780 > 598, we apply the division lemma to 780 and 598, to get
780 = 598 x 1 + 182
Step 2: Since the reminder 598 ≠ 0, we apply division lemma to 182 and 598, to get
598 = 182 x 3 + 52
Step 3: We consider the new divisor 182 and the new remainder 52, and apply the division lemma to get
182 = 52 x 3 + 26
We consider the new divisor 52 and the new remainder 26, and apply the division lemma to get
52 = 26 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 26, the HCF of 780 and 598 is 26
Notice that 26 = HCF(52,26) = HCF(182,52) = HCF(598,182) = HCF(780,598) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 354 > 26, we apply the division lemma to 354 and 26, to get
354 = 26 x 13 + 16
Step 2: Since the reminder 26 ≠ 0, we apply division lemma to 16 and 26, to get
26 = 16 x 1 + 10
Step 3: We consider the new divisor 16 and the new remainder 10, and apply the division lemma to get
16 = 10 x 1 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 26 and 354 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(16,10) = HCF(26,16) = HCF(354,26) .
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Frequently Asked Questions on HCF of 780, 598, 354 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 780, 598, 354?
Answer: HCF of 780, 598, 354 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 780, 598, 354 using Euclid's Algorithm?
Answer: For arbitrary numbers 780, 598, 354 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.