Highest Common Factor of 609, 354, 988 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 609, 354, 988 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 609, 354, 988 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 609, 354, 988 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 609, 354, 988 is 1.
HCF(609, 354, 988) = 1
HCF of 609, 354, 988 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 609, 354, 988 is 1.
Highest Common Factor of 609,354,988 is 1
Step 1: Since 609 > 354, we apply the division lemma to 609 and 354, to get
609 = 354 x 1 + 255
Step 2: Since the reminder 354 ≠ 0, we apply division lemma to 255 and 354, to get
354 = 255 x 1 + 99
Step 3: We consider the new divisor 255 and the new remainder 99, and apply the division lemma to get
255 = 99 x 2 + 57
We consider the new divisor 99 and the new remainder 57,and apply the division lemma to get
99 = 57 x 1 + 42
We consider the new divisor 57 and the new remainder 42,and apply the division lemma to get
57 = 42 x 1 + 15
We consider the new divisor 42 and the new remainder 15,and apply the division lemma to get
42 = 15 x 2 + 12
We consider the new divisor 15 and the new remainder 12,and apply the division lemma to get
15 = 12 x 1 + 3
We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 609 and 354 is 3
Notice that 3 = HCF(12,3) = HCF(15,12) = HCF(42,15) = HCF(57,42) = HCF(99,57) = HCF(255,99) = HCF(354,255) = HCF(609,354) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 988 > 3, we apply the division lemma to 988 and 3, to get
988 = 3 x 329 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 988 is 1
Notice that 1 = HCF(3,1) = HCF(988,3) .
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Frequently Asked Questions on HCF of 609, 354, 988 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 609, 354, 988?
Answer: HCF of 609, 354, 988 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 609, 354, 988 using Euclid's Algorithm?
Answer: For arbitrary numbers 609, 354, 988 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.