Highest Common Factor of 9942, 7035 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 9942, 7035 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 9942, 7035 is 3 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 9942, 7035 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 9942, 7035 is 3.
HCF(9942, 7035) = 3
HCF of 9942, 7035 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9942, 7035 is 3.
Highest Common Factor of 9942,7035 is 3
Step 1: Since 9942 > 7035, we apply the division lemma to 9942 and 7035, to get
9942 = 7035 x 1 + 2907
Step 2: Since the reminder 7035 ≠ 0, we apply division lemma to 2907 and 7035, to get
7035 = 2907 x 2 + 1221
Step 3: We consider the new divisor 2907 and the new remainder 1221, and apply the division lemma to get
2907 = 1221 x 2 + 465
We consider the new divisor 1221 and the new remainder 465,and apply the division lemma to get
1221 = 465 x 2 + 291
We consider the new divisor 465 and the new remainder 291,and apply the division lemma to get
465 = 291 x 1 + 174
We consider the new divisor 291 and the new remainder 174,and apply the division lemma to get
291 = 174 x 1 + 117
We consider the new divisor 174 and the new remainder 117,and apply the division lemma to get
174 = 117 x 1 + 57
We consider the new divisor 117 and the new remainder 57,and apply the division lemma to get
117 = 57 x 2 + 3
We consider the new divisor 57 and the new remainder 3,and apply the division lemma to get
57 = 3 x 19 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 9942 and 7035 is 3
Notice that 3 = HCF(57,3) = HCF(117,57) = HCF(174,117) = HCF(291,174) = HCF(465,291) = HCF(1221,465) = HCF(2907,1221) = HCF(7035,2907) = HCF(9942,7035) .
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Frequently Asked Questions on HCF of 9942, 7035 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 9942, 7035?
Answer: HCF of 9942, 7035 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9942, 7035 using Euclid's Algorithm?
Answer: For arbitrary numbers 9942, 7035 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.