Highest Common Factor of 1002, 738 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 1002, 738 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 1002, 738 is 6 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 1002, 738 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 1002, 738 is 6.
HCF(1002, 738) = 6
HCF of 1002, 738 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1002, 738 is 6.
Highest Common Factor of 1002,738 is 6
Step 1: Since 1002 > 738, we apply the division lemma to 1002 and 738, to get
1002 = 738 x 1 + 264
Step 2: Since the reminder 738 ≠ 0, we apply division lemma to 264 and 738, to get
738 = 264 x 2 + 210
Step 3: We consider the new divisor 264 and the new remainder 210, and apply the division lemma to get
264 = 210 x 1 + 54
We consider the new divisor 210 and the new remainder 54,and apply the division lemma to get
210 = 54 x 3 + 48
We consider the new divisor 54 and the new remainder 48,and apply the division lemma to get
54 = 48 x 1 + 6
We consider the new divisor 48 and the new remainder 6,and apply the division lemma to get
48 = 6 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 1002 and 738 is 6
Notice that 6 = HCF(48,6) = HCF(54,48) = HCF(210,54) = HCF(264,210) = HCF(738,264) = HCF(1002,738) .
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Frequently Asked Questions on HCF of 1002, 738 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 1002, 738?
Answer: HCF of 1002, 738 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1002, 738 using Euclid's Algorithm?
Answer: For arbitrary numbers 1002, 738 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
