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 665, 74676 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 665, 74676 is 7 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 665, 74676 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 665, 74676 is 7.
HCF(665, 74676) = 7
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 665, 74676 is 7.
Step 1: Since 74676 > 665, we apply the division lemma to 74676 and 665, to get
74676 = 665 x 112 + 196
Step 2: Since the reminder 665 ≠ 0, we apply division lemma to 196 and 665, to get
665 = 196 x 3 + 77
Step 3: We consider the new divisor 196 and the new remainder 77, and apply the division lemma to get
196 = 77 x 2 + 42
We consider the new divisor 77 and the new remainder 42,and apply the division lemma to get
77 = 42 x 1 + 35
We consider the new divisor 42 and the new remainder 35,and apply the division lemma to get
42 = 35 x 1 + 7
We consider the new divisor 35 and the new remainder 7,and apply the division lemma to get
35 = 7 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 665 and 74676 is 7
Notice that 7 = HCF(35,7) = HCF(42,35) = HCF(77,42) = HCF(196,77) = HCF(665,196) = HCF(74676,665) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 665, 74676?
Answer: HCF of 665, 74676 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 665, 74676 using Euclid's Algorithm?
Answer: For arbitrary numbers 665, 74676 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.