Highest Common Factor of 986, 374 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 986, 374 i.e. 34 the largest integer that leaves a remainder zero for all numbers.
HCF of 986, 374 is 34 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 986, 374 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 986, 374 is 34.
HCF(986, 374) = 34
HCF of 986, 374 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 986, 374 is 34.
Highest Common Factor of 986,374 is 34
Step 1: Since 986 > 374, we apply the division lemma to 986 and 374, to get
986 = 374 x 2 + 238
Step 2: Since the reminder 374 ≠ 0, we apply division lemma to 238 and 374, to get
374 = 238 x 1 + 136
Step 3: We consider the new divisor 238 and the new remainder 136, and apply the division lemma to get
238 = 136 x 1 + 102
We consider the new divisor 136 and the new remainder 102,and apply the division lemma to get
136 = 102 x 1 + 34
We consider the new divisor 102 and the new remainder 34,and apply the division lemma to get
102 = 34 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 34, the HCF of 986 and 374 is 34
Notice that 34 = HCF(102,34) = HCF(136,102) = HCF(238,136) = HCF(374,238) = HCF(986,374) .
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Frequently Asked Questions on HCF of 986, 374 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 986, 374?
Answer: HCF of 986, 374 is 34 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 986, 374 using Euclid's Algorithm?
Answer: For arbitrary numbers 986, 374 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.