Highest Common Factor of 98, 938, 977 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 98, 938, 977 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 98, 938, 977 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 98, 938, 977 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 98, 938, 977 is 1.
HCF(98, 938, 977) = 1
HCF of 98, 938, 977 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 98, 938, 977 is 1.
Highest Common Factor of 98,938,977 is 1
Step 1: Since 938 > 98, we apply the division lemma to 938 and 98, to get
938 = 98 x 9 + 56
Step 2: Since the reminder 98 ≠ 0, we apply division lemma to 56 and 98, to get
98 = 56 x 1 + 42
Step 3: We consider the new divisor 56 and the new remainder 42, and apply the division lemma to get
56 = 42 x 1 + 14
We consider the new divisor 42 and the new remainder 14, and apply the division lemma to get
42 = 14 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 98 and 938 is 14
Notice that 14 = HCF(42,14) = HCF(56,42) = HCF(98,56) = HCF(938,98) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 977 > 14, we apply the division lemma to 977 and 14, to get
977 = 14 x 69 + 11
Step 2: Since the reminder 14 ≠ 0, we apply division lemma to 11 and 14, to get
14 = 11 x 1 + 3
Step 3: We consider the new divisor 11 and the new remainder 3, and apply the division lemma to get
11 = 3 x 3 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 14 and 977 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(14,11) = HCF(977,14) .
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Frequently Asked Questions on HCF of 98, 938, 977 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 98, 938, 977?
Answer: HCF of 98, 938, 977 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 98, 938, 977 using Euclid's Algorithm?
Answer: For arbitrary numbers 98, 938, 977 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.