Highest Common Factor of 977, 598 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 977, 598 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 977, 598 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 977, 598 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 977, 598 is 1.
HCF(977, 598) = 1
HCF of 977, 598 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 977, 598 is 1.
Highest Common Factor of 977,598 is 1
Step 1: Since 977 > 598, we apply the division lemma to 977 and 598, to get
977 = 598 x 1 + 379
Step 2: Since the reminder 598 ≠ 0, we apply division lemma to 379 and 598, to get
598 = 379 x 1 + 219
Step 3: We consider the new divisor 379 and the new remainder 219, and apply the division lemma to get
379 = 219 x 1 + 160
We consider the new divisor 219 and the new remainder 160,and apply the division lemma to get
219 = 160 x 1 + 59
We consider the new divisor 160 and the new remainder 59,and apply the division lemma to get
160 = 59 x 2 + 42
We consider the new divisor 59 and the new remainder 42,and apply the division lemma to get
59 = 42 x 1 + 17
We consider the new divisor 42 and the new remainder 17,and apply the division lemma to get
42 = 17 x 2 + 8
We consider the new divisor 17 and the new remainder 8,and apply the division lemma to get
17 = 8 x 2 + 1
We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get
8 = 1 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 977 and 598 is 1
Notice that 1 = HCF(8,1) = HCF(17,8) = HCF(42,17) = HCF(59,42) = HCF(160,59) = HCF(219,160) = HCF(379,219) = HCF(598,379) = HCF(977,598) .
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Frequently Asked Questions on HCF of 977, 598 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 977, 598?
Answer: HCF of 977, 598 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 977, 598 using Euclid's Algorithm?
Answer: For arbitrary numbers 977, 598 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.