Highest Common Factor of 98, 735, 137 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, 735, 137 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 98, 735, 137 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, 735, 137 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, 735, 137 is 1.
HCF(98, 735, 137) = 1
HCF of 98, 735, 137 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, 735, 137 is 1.
Highest Common Factor of 98,735,137 is 1
Step 1: Since 735 > 98, we apply the division lemma to 735 and 98, to get
735 = 98 x 7 + 49
Step 2: Since the reminder 98 ≠ 0, we apply division lemma to 49 and 98, to get
98 = 49 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 49, the HCF of 98 and 735 is 49
Notice that 49 = HCF(98,49) = HCF(735,98) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 137 > 49, we apply the division lemma to 137 and 49, to get
137 = 49 x 2 + 39
Step 2: Since the reminder 49 ≠ 0, we apply division lemma to 39 and 49, to get
49 = 39 x 1 + 10
Step 3: We consider the new divisor 39 and the new remainder 10, and apply the division lemma to get
39 = 10 x 3 + 9
We consider the new divisor 10 and the new remainder 9,and apply the division lemma to get
10 = 9 x 1 + 1
We consider the new divisor 9 and the new remainder 1,and apply the division lemma to get
9 = 1 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 49 and 137 is 1
Notice that 1 = HCF(9,1) = HCF(10,9) = HCF(39,10) = HCF(49,39) = HCF(137,49) .
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Frequently Asked Questions on HCF of 98, 735, 137 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, 735, 137?
Answer: HCF of 98, 735, 137 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 98, 735, 137 using Euclid's Algorithm?
Answer: For arbitrary numbers 98, 735, 137 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.